Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of type complex or real of arbitrary kind parameter. More...

Detailed Description

Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of type complex or real of arbitrary kind parameter.

See the documentation of pm_fftnr for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of size getExpNext(size(data), 2) of the same type and kind as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftnr, only: getFFTF

type_of(data) :: fft(1 : getExpNext(size(data)))

fft(:) = getFFTF(data(:))

pm_fftnr::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250

pm_fftnr
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftnr.F90:184

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTF.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftnr, only: getFFTF, getFFTI

6 use pm_distUnif, only: getUnifRand

7 use pm_mathCompare, only: isClose

8 use pm_err, only: setAsserted

9

10 implicit none

11

12 integer(IK) :: i

13 integer(IK) :: lenData

14 type(display_type) :: disp

15 disp = display_type(file = "main.out.F90")

16

17 do i = 1, 5

18 block

19 use pm_kind, only: TKC => CKS

20 real(TKC) :: reltol

21 complex(TKC), allocatable :: data(:), atad(:)

22 call disp%show("lenData = getUnifRand(5, 100)")

23 lenData = getUnifRand(5, 100)

24 call disp%show("lenData")

25 call disp%show( lenData )

26 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

27 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

28 call disp%show("data")

29 call disp%show( data )

30 call disp%skip()

31 call disp%show("atad = getFFTI(getFFTF(data))")

32 atad = getFFTI(getFFTF(data))

33 call disp%show("atad")

34 call disp%show( atad )

35 call disp%show("reltol = sqrt(epsilon(1._TKC))")

36 reltol = sqrt(epsilon(1._TKC))

37 call disp%show("reltol")

38 call disp%show( reltol )

39 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

40 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

41 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

42 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

43 call disp%skip()

44 end block

45

46 block

47 use pm_kind, only: TKC => CKD

48 real(TKC) :: reltol

49 complex(TKC), allocatable :: data(:), atad(:)

50 call disp%show("lenData = getUnifRand(5, 100)")

51 lenData = getUnifRand(5, 100)

52 call disp%show("lenData")

53 call disp%show( lenData )

54 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

55 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

56 call disp%show("data")

57 call disp%show( data )

58 call disp%skip()

59 call disp%show("atad = getFFTI(getFFTF(data))")

60 atad = getFFTI(getFFTF(data))

61 call disp%show("atad")

62 call disp%show( atad )

63 call disp%show("reltol = sqrt(epsilon(1._TKC))")

64 reltol = sqrt(epsilon(1._TKC))

65 call disp%show("reltol")

66 call disp%show( reltol )

67 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

68 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

69 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

70 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

71 call disp%skip()

72 end block

73

74 block

75 use pm_kind, only: TKC => CKH

76 real(TKC) :: reltol

77 complex(TKC), allocatable :: data(:), atad(:)

78 call disp%show("lenData = getUnifRand(5, 100)")

79 lenData = getUnifRand(5, 100)

80 call disp%show("lenData")

81 call disp%show( lenData )

82 call disp%show("data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)")

83 data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

84 call disp%show("data")

85 call disp%show( data )

86 call disp%skip()

87 call disp%show("atad = getFFTI(getFFTF(data))")

88 atad = getFFTI(getFFTF(data))

89 call disp%show("atad")

90 call disp%show( atad )

91 call disp%show("reltol = sqrt(epsilon(1._TKC))")

92 reltol = sqrt(epsilon(1._TKC))

93 call disp%show("reltol")

94 call disp%show( reltol )

95 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

96 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

97 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

98 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

99 call disp%skip()

100 end block

101

102 block

103 use pm_kind, only: TKC => RKS

104 real(TKC) :: reltol

105 real(TKC), allocatable :: data(:), atad(:)

106 call disp%show("lenData = getUnifRand(5, 100)")

107 lenData = getUnifRand(5, 100)

108 call disp%show("lenData")

109 call disp%show( lenData )

110 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

111 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

112 call disp%show("data")

113 call disp%show( data )

114 call disp%skip()

115 call disp%show("atad = getFFTI(getFFTF(data))")

116 atad = getFFTI(getFFTF(data))

117 call disp%show("atad")

118 call disp%show( atad )

119 call disp%show("reltol = sqrt(epsilon(1._TKC))")

120 reltol = sqrt(epsilon(1._TKC))

121 call disp%show("reltol")

122 call disp%show( reltol )

123 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

124 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

125 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

126 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

127 call disp%skip()

128 end block

129

130 block

131 use pm_kind, only: TKC => RKD

132 real(TKC) :: reltol

133 real(TKC), allocatable :: data(:), atad(:)

134 call disp%show("lenData = getUnifRand(5, 100)")

135 lenData = getUnifRand(5, 100)

136 call disp%show("lenData")

137 call disp%show( lenData )

138 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

139 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

140 call disp%show("data")

141 call disp%show( data )

142 call disp%skip()

143 call disp%show("atad = getFFTI(getFFTF(data))")

144 atad = getFFTI(getFFTF(data))

145 call disp%show("atad")

146 call disp%show( atad )

147 call disp%show("reltol = sqrt(epsilon(1._TKC))")

148 reltol = sqrt(epsilon(1._TKC))

149 call disp%show("reltol")

150 call disp%show( reltol )

151 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

152 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

153 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

154 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

155 call disp%skip()

156 end block

157

158 block

159 use pm_kind, only: TKC => RKH

160 real(TKC) :: reltol

161 real(TKC), allocatable :: data(:), atad(:)

162 call disp%show("lenData = getUnifRand(5, 100)")

163 lenData = getUnifRand(5, 100)

164 call disp%show("lenData")

165 call disp%show( lenData )

166 call disp%show("data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)")

167 data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

168 call disp%show("data")

169 call disp%show( data )

170 call disp%skip()

171 call disp%show("atad = getFFTI(getFFTF(data))")

172 atad = getFFTI(getFFTF(data))

173 call disp%show("atad")

174 call disp%show( atad )

175 call disp%show("reltol = sqrt(epsilon(1._TKC))")

176 reltol = sqrt(epsilon(1._TKC))

177 call disp%show("reltol")

178 call disp%show( reltol )

179 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

180 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

181 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

182 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

183 call disp%skip()

184 end block

185 end do

186

187end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4106

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftnr::getFFTI
Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequen...
Definition: pm_fftnr.F90:428

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11074

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:523

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:10962

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:28

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:281

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:477

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:310

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:280

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:311

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:308

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:279

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind a...
Definition: pm_kind.F90:462

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:307

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10228

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_intel* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte_fortran_*_intel*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte_fortran_*_gnu* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+49

4data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

5data

6(+1.26376605, +0.753055751), (+1.36109591, +0.678411722E-1), (+1.75238132, +0.336624444), (+1.87275743, +0.813802302), (+1.54128003, +0.487934113), (+1.16697431, +0.994305372), (+1.48693538, +0.935363889), (+1.45654941, +0.162711084), (+1.57055020, +0.681066513), (+1.19317138, +0.515210927), (+1.86117148, +0.856274724), (+1.73258829, +0.653773606), (+1.65570223, +0.781163216), (+1.22884166, +0.183632970E-1), (+1.50443363, +0.769660890), (+1.17717731, +0.339377463), (+1.69401991, +0.770092368), (+1.17039895, +0.463918090), (+1.60610092, +0.586601794), (+1.95211029, +0.200305521), (+1.70322943, +0.417850316), (+1.62902188, +0.423272789), (+1.45248127, +0.299959540), (+1.70776546, +0.554145575), (+1.80778503, +0.224880934), (+1.13828373, +0.427255034), (+1.15300822, +0.364711702), (+1.53274393, +0.354721010), (+1.21487522, +0.298198283), (+1.93231571, +0.465855241), (+1.39100552, +0.302361965), (+1.40670264, +0.190537751), (+1.11498356, +0.165844917), (+1.60656404, +0.927889526), (+1.66557813, +0.552790821), (+1.56300068, +0.221580088), (+1.98257923, +0.765868425), (+1.07235360, +0.417106926), (+1.91746533, +0.347639978), (+1.83442247, +0.271938562), (+1.63798785, +0.270699263E-1), (+1.24264538, +0.862135887E-1), (+1.36802292, +0.102063477), (+1.83434629, +0.737508714), (+1.24465466, +0.547491908E-1), (+1.86178923, +0.746077418), (+1.59537721, +0.455182791E-2), (+1.20592713, +0.387368441), (+1.44828105, +0.575212717)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.26376617, +0.753055751), (+1.36109567, +0.678412616E-1), (+1.75238109, +0.336624354), (+1.87275732, +0.813802242), (+1.54128015, +0.487934291), (+1.16697407, +0.994305432), (+1.48693538, +0.935363650), (+1.45654929, +0.162711084), (+1.57055020, +0.681066513), (+1.19317114, +0.515210986), (+1.86117148, +0.856274605), (+1.73258829, +0.653773546), (+1.65570211, +0.781163335), (+1.22884166, +0.183635056E-1), (+1.50443363, +0.769660890), (+1.17717731, +0.339377701), (+1.69401991, +0.770092368), (+1.17039871, +0.463918179), (+1.60610104, +0.586601734), (+1.95211029, +0.200305521), (+1.70322943, +0.417850345), (+1.62902164, +0.423272789), (+1.45248127, +0.299959540), (+1.70776558, +0.554145575), (+1.80778503, +0.224880934), (+1.13828373, +0.427255034), (+1.15300846, +0.364711642), (+1.53274393, +0.354721069), (+1.21487534, +0.298198313), (+1.93231535, +0.465855420), (+1.39100552, +0.302361906), (+1.40670252, +0.190537900), (+1.11498368, +0.165844977), (+1.60656381, +0.927889347), (+1.66557813, +0.552790701), (+1.56300080, +0.221579999), (+1.98257935, +0.765868485), (+1.07235336, +0.417106807), (+1.91746545, +0.347639948), (+1.83442223, +0.271938473), (+1.63798785, +0.270699561E-1), (+1.24264514, +0.862135887E-1), (+1.36802316, +0.102063507), (+1.83434629, +0.737508535), (+1.24465466, +0.547492802E-1), (+1.86178887, +0.746077299), (+1.59537721, +0.455200672E-2), (+1.20592725, +0.387368381), (+1.44828117, +0.575212598), (-0.596046448E-7, +0.298023224E-7), (+0.357627869E-6, +0.894069672E-7), (+0.417232513E-6, +0.298023224E-6), (+0.119209290E-6, -0.149011612E-6), (+0.596046448E-7, +0.104308128E-6), (+0.298023224E-6, +0.223517418E-6), (+0.298023224E-6, +0.238418579E-6), (+0.417232513E-6, +0.745058060E-8), (+0.178813934E-6, -0.149011612E-7), (+0.417232513E-6, +0.134110451E-6), (+0.417232513E-6, +0.745058060E-7), (+0.238418579E-6, -0.149011612E-6), (+0.357627869E-6, -0.253319740E-6), (+0.238418579E-6, -0.104308128E-6), (-0.596046448E-7, -0.596046448E-7)

11reltol = sqrt(epsilon(1._TKC))

12reltol

13+0.345266977E-3

14isClose(data, atad(1:size(data)), reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+20

21data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

22data

23(+1.4359675865931565, +0.68894006240566741E-1), (+1.7328308914229853, +0.52894416179302017), (+1.5904913424300453, +0.70965957547584402), (+1.5190251644782338, +0.52679417116849137), (+1.5872036172091657, +0.19496951869490442), (+1.5155444580429127, +0.10698526529252284), (+1.6143078487584210, +0.40984155310646886), (+1.5818222589451201, +0.34576604502761954), (+1.4970259114558790, +0.66614374399637999), (+1.8845127905272232, +0.34688542579963200), (+1.6934960824752840, +0.87761281721302487), (+1.2363222697519700, +0.33849105516402300), (+1.4417004042124510, +0.90633361679573710), (+1.8492461651735652, +0.26801868610528046), (+1.8381195227118967, +0.55070842486818306), (+1.7125980246761761, +0.99826934502309672), (+1.0102123698949499, +0.12135459961047079), (+1.0384737225440275, +0.28965828218065826), (+1.2111068692559521, +0.50035497343598934), (+1.2058201141576654, +0.40791703700178239)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.4359675865931565, +0.68894006240566713E-1), (+1.7328308914229853, +0.52894416179302017), (+1.5904913424300455, +0.70965957547584402), (+1.5190251644782338, +0.52679417116849159), (+1.5872036172091655, +0.19496951869490453), (+1.5155444580429127, +0.10698526529252296), (+1.6143078487584208, +0.40984155310646897), (+1.5818222589451194, +0.34576604502761954), (+1.4970259114558790, +0.66614374399637977), (+1.8845127905272228, +0.34688542579963177), (+1.6934960824752840, +0.87761281721302475), (+1.2363222697519698, +0.33849105516402289), (+1.4417004042124506, +0.90633361679573676), (+1.8492461651735648, +0.26801868610528012), (+1.8381195227118967, +0.55070842486818283), (+1.7125980246761756, +0.99826934502309572), (+1.0102123698949499, +0.12135459961047088), (+1.0384737225440277, +0.28965828218065809), (+1.2111068692559523, +0.50035497343598945), (+1.2058201141576657, +0.40791703700178195), (+0.22204460492503131E-15, +0.0000000000000000), (+0.55511151231257827E-15, -0.20816681711721685E-15), (+0.44408920985006262E-15, -0.11102230246251565E-15), (+0.77715611723760958E-15, +0.0000000000000000), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.44408920985006262E-15, -0.83266726846886741E-16), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.44408920985006262E-15, +0.83266726846886741E-16), (+0.33306690738754696E-15, +0.22204460492503131E-15), (+0.66613381477509392E-15, +0.33306690738754696E-15), (+0.33306690738754696E-15, +0.27755575615628914E-15), (+0.55511151231257827E-15, +0.72164496600635175E-15)

28reltol = sqrt(epsilon(1._TKC))

29reltol

30+0.14901161193847656E-7

31isClose(data, atad(1:size(data)), reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+47

38data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

39data

40(+1.03128634430156548906839572974789251, +0.141740397737125693718490403434530418), (+1.95385791851680351769244975601212387, +0.436648975570444616821195815283587874), (+1.75262497885185282444592070645710594, +0.867916810752735348511458425646463396), (+1.22976336546054646505361358355267631, +0.973056181840544728195861993681639706), (+1.49068116178776986310375532384646561, +0.174789698897038874360428653366488708), (+1.30673528957720176395418666697726737, +0.172049171124520940755813613259573319), (+1.46206220411031110020745131591696981, +0.407759612796343161822538342191303487), (+1.29513874530777329433964250208561411, +0.123514296257719722995635341083416449), (+1.03115663586011356504405467982990911, +0.149542652136626708020221531749725918), (+1.27599059071022791541022656431477787, +0.857783926366145507530042186599665829), (+1.09292604084134908073011010803591313, +0.820863314146933142260090684878116056), (+1.72150434722398952024849485525665057, +0.221453751394127502363776883306667818), (+1.10379508030218597773284057425576327, +0.296532152580098553988554224966185938), (+1.85235286260156428898155480410709672, +0.641479088350082448757374106882572077), (+1.87085413161330863025757049805660090, +0.655356925474289868241079241352662614), (+1.60617904588839073905090858932458734, +0.399875358932042258814568591051530252), (+1.53928208150296269938225563014512947, +0.891519613903315177855226051149084234), (+1.21190580652795963447249631594441539, +0.492760533582296504074011754795835157), (+1.28749198724662603448094884504615475, +0.628378742325239131236819265111842978E-1), (+1.51451112135279115597783119841250599, +0.267895016223317596077540036780950383), (+1.34210715774329311822971043597878838, +0.877341826224546198425988948942731730), (+1.61613342772797879376715818137871510, +0.619671185303095116440951663298772749), (+1.79678939097384492271525332530975545, +0.872156402143428051872763577520036403), (+1.70286033541733381427711375028814188, +0.135669491584833604616995507343302695E-1), (+1.63012515203956946509798966532134648, +0.840340168656007941099620424730647250), (+1.04784499918737394246079325664019191, +0.827228468382544895898821400618286280), (+1.29333535915479456740819865172339228, +0.352102385983636109048419525232548079), (+1.48381754295037194972924010678487016, +0.835986272459060999911178001619954288), (+1.70214139344426197677847139440746261, +0.694537729398273547462025542561736074), (+1.04036095386665483255607429797778939, +0.459015389388575249450925390167347996), (+1.27286333106546563885309296944131855, +0.477049018314819611594758247688753584), (+1.67177460359800607980516624896518868, +0.374188906299867643660082198710509910), (+1.32208845239434597926084209235243661, +0.710632815527300841748877070490765932), (+1.22039796887477381607819227414567553, +0.149833149521092194987642636657251080), (+1.61914241820357175305457600380405927, +0.201507126655592880219972821384290223), (+1.88121075112469717601193362338727256, +0.558503730093584408326502496177012483), (+1.04456463851858519331300862037545797, +0.708108222284560829029840560440132202), (+1.62727263344869921574477233662494157, +0.353775480930854037329615760073349799), (+1.83902270684022035676720373617251605, +0.184843376923723798156887792053714247), (+1.70675826050033290439253376662202071, +0.854466458492441092453164811538329641), (+1.76024308815389879533878516311947873, +0.128544538230055385658017272259503816), (+1.23488494460546696380302101417638968, +0.544015909551422573323917433288694628), (+1.60395531313400295138123309419256891, +0.197152428081028477990423883199135030), (+1.63155021119045427072040563586462783, +0.925353264044821846380257794745011304), (+1.14503619656845841391438894854927278, +0.976565805143947671416799347752188271), (+1.76456852505976899198636349088882117, +0.592441897910906050540925465084044737), (+1.50347912726822753763681582291748752, +0.432380104684483496242582478868124237)

41

42atad = getFFTI(getFFTF(data))

43atad

44(+1.03128634430156548906839572974789213, +0.141740397737125693718490403434530418), (+1.95385791851680351769244975601212367, +0.436648975570444616821195815283587971), (+1.75262497885185282444592070645710556, +0.867916810752735348511458425646463300), (+1.22976336546054646505361358355267592, +0.973056181840544728195861993681639802), (+1.49068116178776986310375532384646580, +0.174789698897038874360428653366488515), (+1.30673528957720176395418666697726718, +0.172049171124520940755813613259573271), (+1.46206220411031110020745131591696981, +0.407759612796343161822538342191303198), (+1.29513874530777329433964250208561411, +0.123514296257719722995635341083416304), (+1.03115663586011356504405467982990873, +0.149542652136626708020221531749726015), (+1.27599059071022791541022656431477748, +0.857783926366145507530042186599665925), (+1.09292604084134908073011010803591294, +0.820863314146933142260090684878115959), (+1.72150434722398952024849485525665018, +0.221453751394127502363776883306668058), (+1.10379508030218597773284057425576346, +0.296532152580098553988554224966186227), (+1.85235286260156428898155480410709672, +0.641479088350082448757374106882572270), (+1.87085413161330863025757049805660071, +0.655356925474289868241079241352662710), (+1.60617904588839073905090858932458734, +0.399875358932042258814568591051530348), (+1.53928208150296269938225563014512908, +0.891519613903315177855226051149084234), (+1.21190580652795963447249631594441520, +0.492760533582296504074011754795835157), (+1.28749198724662603448094884504615436, +0.628378742325239131236819265111841775E-1), (+1.51451112135279115597783119841250599, +0.267895016223317596077540036780950190), (+1.34210715774329311822971043597878838, +0.877341826224546198425988948942731922), (+1.61613342772797879376715818137871491, +0.619671185303095116440951663298772653), (+1.79678939097384492271525332530975526, +0.872156402143428051872763577520036211), (+1.70286033541733381427711375028814188, +0.135669491584833604616995507343300047E-1), (+1.63012515203956946509798966532134629, +0.840340168656007941099620424730647153), (+1.04784499918737394246079325664019172, +0.827228468382544895898821400618286184), (+1.29333535915479456740819865172339228, +0.352102385983636109048419525232547887), (+1.48381754295037194972924010678486997, +0.835986272459060999911178001619953999), (+1.70214139344426197677847139440746261, +0.694537729398273547462025542561736170), (+1.04036095386665483255607429797778939, +0.459015389388575249450925390167347804), (+1.27286333106546563885309296944131855, +0.477049018314819611594758247688753392), (+1.67177460359800607980516624896518868, +0.374188906299867643660082198710509910), (+1.32208845239434597926084209235243623, +0.710632815527300841748877070490765932), (+1.22039796887477381607819227414567534, +0.149833149521092194987642636657251008), (+1.61914241820357175305457600380405889, +0.201507126655592880219972821384290030), (+1.88121075112469717601193362338727236, +0.558503730093584408326502496177012387), (+1.04456463851858519331300862037545797, +0.708108222284560829029840560440132299), (+1.62727263344869921574477233662494157, +0.353775480930854037329615760073349751), (+1.83902270684022035676720373617251586, +0.184843376923723798156887792053714175), (+1.70675826050033290439253376662202071, +0.854466458492441092453164811538329929), (+1.76024308815389879533878516311947835, +0.128544538230055385658017272259503720), (+1.23488494460546696380302101417638949, +0.544015909551422573323917433288694436), (+1.60395531313400295138123309419256871, +0.197152428081028477990423883199134982), (+1.63155021119045427072040563586462783, +0.925353264044821846380257794745010919), (+1.14503619656845841391438894854927239, +0.976565805143947671416799347752188367), (+1.76456852505976899198636349088882117, +0.592441897910906050540925465084045026), (+1.50347912726822753763681582291748732, +0.432380104684483496242582478868124333), (-0.192592994438723585305597794258492732E-33, +0.722223729145213444895991728469347744E-34), (-0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, -0.216667118743564033468797518540804323E-33), (-0.962964972193617926527988971292463659E-34, +0.120370621524202240815998621411557957E-33), (+0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (-0.481482486096808963263994485646231830E-33, -0.481482486096808963263994485646231830E-34), (-0.577778983316170755916793382775478196E-33, +0.144444745829042688979198345693869549E-33), (+0.192592994438723585305597794258492732E-33, +0.216667118743564033468797518540804323E-33), (-0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34), (+0.962964972193617926527988971292463659E-34, +0.216667118743564033468797518540804323E-33), (+0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33), (+0.00000000000000000000000000000000000, -0.457408361791968515100794761363920238E-33), (-0.288889491658085377958396691387739098E-33, -0.120370621524202240815998621411557957E-33), (-0.962964972193617926527988971292463659E-34, +0.722223729145213444895991728469347744E-34)

45reltol = sqrt(epsilon(1._TKC))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, atad(1:size(data)), reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+34

55data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

56data

57+1.45220220, +1.74827671, +1.80569208, +1.45093465, +1.89140868, +1.96813107, +1.30967283, +1.65846193, +1.55308700, +1.37562037, +1.34272766, +1.68779528, +1.29561901, +1.75506091, +1.93165839, +1.50473237, +1.29699969, +1.19496059, +1.47725153, +1.70295739, +1.79235268, +1.65973461, +1.52861965, +1.14354455, +1.15902567, +1.28401601, +1.78345823, +1.84639168, +1.53942788, +1.99216533, +1.37016034, +1.59730244, +1.99197721, +1.46006286

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.45220232, +1.74827671, +1.80569220, +1.45093441, +1.89140868, +1.96813095, +1.30967283, +1.65846181, +1.55308676, +1.37562037, +1.34272790, +1.68779516, +1.29561889, +1.75506091, +1.93165839, +1.50473213, +1.29699981, +1.19496059, +1.47725177, +1.70295727, +1.79235268, +1.65973473, +1.52861977, +1.14354455, +1.15902555, +1.28401613, +1.78345823, +1.84639144, +1.53942788, +1.99216509, +1.37016034, +1.59730220, +1.99197721, +1.46006298, +0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.00000000, +0.596046448E-7, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, -0.596046448E-7, +0.00000000, +0.357627869E-6, -0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.00000000, +0.119209290E-6, -0.596046448E-7, +0.00000000, +0.178813934E-6, -0.596046448E-7, +0.596046448E-7, -0.119209290E-6, +0.119209290E-6, -0.596046448E-7, +0.119209290E-6, +0.00000000, +0.119209290E-6, +0.119209290E-6, +0.238418579E-6, +0.119209290E-6

62reltol = sqrt(epsilon(1._TKC))

63reltol

64+0.345266977E-3

65isClose(data, atad(1:size(data)), reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+53

72data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

73data

74+1.2981441292653735, +1.2199607323650978, +1.1927692611010512, +1.2127360476938633, +1.3100663481871404, +1.3257877782289438, +1.8209627719623140, +1.8821591717178268, +1.0430571900447796, +1.3908564820322109, +1.3745849936289511, +1.3117582319131287, +1.6375836937451633, +1.9140153920588761, +1.8028335090295549, +1.0226981199734093, +1.3721800810251188, +1.0094667190010520, +1.9887780312692958, +1.5860565528116237, +1.9380091311354031, +1.6985991032847449, +1.2255665877006443, +1.7484767064262050, +1.0041706049247636, +1.0129128045788738, +1.1053615475868162, +1.7384364905422904, +1.0969353814926357, +1.4684515035916679, +1.9216064152440424, +1.8578014148297841, +1.5235898507081465, +1.3181604654519468, +1.1759493787252047, +1.5258975062997271, +1.5407465531535993, +1.7119890018539052, +1.6156301028606683, +1.1315082622793542, +1.9193370274431403, +1.2496773751144528, +1.0132739479471145, +1.3910199720852452, +1.4710513233648361, +1.2708794151541358, +1.1511373786079653, +1.5079181817086842, +1.8275853736464502, +1.3731568319879710, +1.2052945900501397, +1.8550775561430826, +1.1776490382239084

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.2981441292653733, +1.2199607323650978, +1.1927692611010512, +1.2127360476938636, +1.3100663481871404, +1.3257877782289438, +1.8209627719623140, +1.8821591717178268, +1.0430571900447794, +1.3908564820322102, +1.3745849936289511, +1.3117582319131289, +1.6375836937451631, +1.9140153920588761, +1.8028335090295549, +1.0226981199734095, +1.3721800810251186, +1.0094667190010518, +1.9887780312692955, +1.5860565528116239, +1.9380091311354031, +1.6985991032847445, +1.2255665877006443, +1.7484767064262043, +1.0041706049247634, +1.0129128045788729, +1.1053615475868162, +1.7384364905422900, +1.0969353814926357, +1.4684515035916674, +1.9216064152440424, +1.8578014148297828, +1.5235898507081465, +1.3181604654519465, +1.1759493787252047, +1.5258975062997271, +1.5407465531535993, +1.7119890018539052, +1.6156301028606685, +1.1315082622793540, +1.9193370274431401, +1.2496773751144523, +1.0132739479471145, +1.3910199720852456, +1.4710513233648361, +1.2708794151541358, +1.1511373786079659, +1.5079181817086837, +1.8275853736464500, +1.3731568319879708, +1.2052945900501402, +1.8550775561430826, +1.1776490382239087, +0.22204460492503131E-15, +0.12212453270876722E-14, +0.0000000000000000, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.55511151231257827E-15, +0.99920072216264089E-15, +0.88817841970012523E-15, +0.44408920985006262E-15, +0.88817841970012523E-15, +0.77715611723760958E-15

79reltol = sqrt(epsilon(1._TKC))

80reltol

81+0.14901161193847656E-7

82isClose(data, atad(1:size(data)), reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+26

89data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

90data

91+1.69095007935452131881388980260433752, +1.75400631627848041211362086955809049, +1.10630545256492274163629269514983386, +1.51693430840422024687404922178510984, +1.19954263193991773225583899511327353, +1.71298242689384834680731201217936448, +1.02378238604876598759462216959865842, +1.45361359979056895542929480775081081, +1.41977162581972309571917432064924672, +1.53335972974327253721034956501419828, +1.42887561697214269057471966958586965, +1.17394500127950158741384010004182599, +1.22780031645367087010934427870846954, +1.23315785339894233858335512362684062, +1.44708785292439155623520898958548696, +1.32575570338295781513698981637413569, +1.09200047016794557356330862820910385, +1.00689252509757903226287681880732464, +1.83664365622258347958492016423116274, +1.44693774957600304967312661117692732, +1.53532435669236014443916073955401952, +1.36158766104567149815576529898137050, +1.77335920738892291272021826550634330, +1.11608047661247176536477816510243195, +1.72941617240720076161233273244632192, +1.78469727074660329162758677870036907

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.69095007935452131881388980260433733, +1.75400631627848041211362086955809049, +1.10630545256492274163629269514983367, +1.51693430840422024687404922178511003, +1.19954263193991773225583899511327334, +1.71298242689384834680731201217936410, +1.02378238604876598759462216959865842, +1.45361359979056895542929480775081119, +1.41977162581972309571917432064924653, +1.53335972974327253721034956501419848, +1.42887561697214269057471966958586965, +1.17394500127950158741384010004182637, +1.22780031645367087010934427870846992, +1.23315785339894233858335512362684043, +1.44708785292439155623520898958548716, +1.32575570338295781513698981637413569, +1.09200047016794557356330862820910365, +1.00689252509757903226287681880732503, +1.83664365622258347958492016423116216, +1.44693774957600304967312661117692770, +1.53532435669236014443916073955401933, +1.36158766104567149815576529898137050, +1.77335920738892291272021826550634291, +1.11608047661247176536477816510243195, +1.72941617240720076161233273244632173, +1.78469727074660329162758677870036907, -0.770371977754894341222391177033970927E-33, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33, -0.962964972193617926527988971292463659E-34

96reltol = sqrt(epsilon(1._TKC))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, atad(1:size(data)), reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+40

106data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

107data

108(+1.93459344, +0.318854272), (+1.80893183, +0.872747183), (+1.92832732, +0.698730826), (+1.86570764, +0.650531352), (+1.08174074, +0.463620663), (+1.21172380, +0.506960213), (+1.77437401, +0.170798838), (+1.56355119, +0.181504250), (+1.35115147, +0.301960170), (+1.24416614, +0.516029179), (+1.69283700, +0.256065071), (+1.47647715, +0.594330728), (+1.43969238, +0.509750843E-1), (+1.64110661, +0.390488327), (+1.94453394, +0.115474164), (+1.30100107, +0.708339691), (+1.57402635, +0.129440665), (+1.61771822, +0.216501713), (+1.53377247, +0.656817973), (+1.90184069, +0.636347950), (+1.08331287, +0.551143289), (+1.17925477, +0.620802104), (+1.77724671, +0.338815570), (+1.56917870, +0.502816856), (+1.14776969, +0.832417667), (+1.32276571, +0.358983219), (+1.02962995, +0.485687792), (+1.75100350, +0.648381174), (+1.83569074, +0.847760201), (+1.17071915, +0.815302432), (+1.55941033, +0.327843785), (+1.51142716, +0.497979760), (+1.90305042, +0.920207322), (+1.72300255, +0.561440587), (+1.79553103, +0.639521837), (+1.53182769, +0.417154074), (+1.14892101, +0.493072629), (+1.22848988, +0.758337975E-2), (+1.05053639, +0.547688425), (+1.90456891, +0.231948674)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.93459344, +0.318854332), (+1.80893171, +0.872747183), (+1.92832708, +0.698730826), (+1.86570716, +0.650531292), (+1.08174086, +0.463620633), (+1.21172380, +0.506960154), (+1.77437401, +0.170798749), (+1.56355095, +0.181504190), (+1.35115123, +0.301960349), (+1.24416590, +0.516029239), (+1.69283700, +0.256065190), (+1.47647679, +0.594330847), (+1.43969226, +0.509753376E-1), (+1.64110637, +0.390488625), (+1.94453382, +0.115474291), (+1.30100095, +0.708339810), (+1.57402623, +0.129440695), (+1.61771822, +0.216501713), (+1.53377247, +0.656817794), (+1.90184045, +0.636347771), (+1.08331275, +0.551143289), (+1.17925477, +0.620802045), (+1.77724671, +0.338815540), (+1.56917858, +0.502816677), (+1.14776945, +0.832417607), (+1.32276547, +0.358983189), (+1.02962995, +0.485687733), (+1.75100327, +0.648380935), (+1.83569014, +0.847760201), (+1.17071891, +0.815302134), (+1.55941010, +0.327843904), (+1.51142704, +0.497979581), (+1.90305042, +0.920207262), (+1.72300255, +0.561440468), (+1.79553127, +0.639521599), (+1.53182769, +0.417153925), (+1.14892101, +0.493072659), (+1.22848988, +0.758333504E-2), (+1.05053663, +0.547688365), (+1.90456915, +0.231948495), (+0.596046448E-7, -0.178813934E-6), (+0.178813934E-6, -0.149011612E-6), (+0.298023224E-6, +0.447034836E-7), (+0.596046448E-6, -0.596046448E-7), (+0.00000000, -0.223517418E-6), (+0.238418579E-6, -0.134110451E-6), (+0.178813934E-6, -0.521540642E-7), (+0.238418579E-6, -0.596046448E-7), (+0.119209290E-6, +0.372529030E-7), (+0.119209290E-6, +0.00000000), (+0.596046448E-7, +0.268220901E-6), (+0.178813934E-6, +0.268220901E-6), (+0.596046448E-7, +0.00000000), (+0.238418579E-6, -0.298023224E-7), (+0.238418579E-6, +0.298023224E-7), (+0.596046448E-7, +0.149011612E-6), (+0.119209290E-6, +0.894069672E-7), (+0.119209290E-6, +0.894069672E-7), (+0.178813934E-6, +0.193715096E-6), (+0.238418579E-6, +0.417232513E-6), (+0.357627869E-6, -0.119209290E-6), (+0.298023224E-6, +0.894069672E-7), (+0.178813934E-6, -0.745058060E-7), (-0.238418579E-6, +0.253319740E-6)

113reltol = sqrt(epsilon(1._TKC))

114reltol

115+0.345266977E-3

116isClose(data, atad(1:size(data)), reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+86

123data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

124data

125(+1.7963104043559004, +0.10637082583187507), (+1.3069909152188863, +0.11836222327626145), (+1.8137206778307307, +0.65940581336449589), (+1.3110129993266235, +0.65040336286904066), (+1.9785225545125984, +0.78919912787531465), (+1.2690542392905353, +0.77966450369900708), (+1.5237971366481011, +0.64573457843489834), (+1.3280509241619289, +0.98220876961150683), (+1.7676089004834050, +0.50279080753382388E-1), (+1.3865365798091394, +0.82906989800056674), (+1.3060701071461229, +0.59584524086238499), (+1.5326350665249593, +0.46874638377425881), (+1.6245288016258552, +0.38157049243912644), (+1.0079837011915664, +0.30208203059722460), (+1.8539531626790386, +0.11082913353240320), (+1.4838454603576614, +0.70229485099907363), (+1.4107020464127000, +0.75393800781390530), (+1.1860888312137223, +0.88822744465302050), (+1.9456789446281550, +0.35288111988647319), (+1.2491143363315165, +0.43875506116692164), (+1.5717684971127133, +0.28205932044632465), (+1.6322904079047476, +0.17167445275799875), (+1.0131550590235272, +0.68449789793036342), (+1.4741874324919713, +0.42188376734337441), (+1.1946800324062128, +0.79913418573006767), (+1.9190926424822876, +0.35064826348427669E-1), (+1.8408845798681053, +0.94136770889401722), (+1.5145350195923220, +0.14128110595632770), (+1.9988769877153016, +0.42841927300002514), (+1.7960335650452381, +0.44922130423344542), (+1.3483263408664432, +0.15748171573241243), (+1.7228816993266380, +0.14183493641309985), (+1.8108421882871477, +0.95924609083743340E-1), (+1.2775908015251001, +0.38666190424747504), (+1.6219108123861927, +0.47646618116515049), (+1.6500750308521022, +0.91064757380676042), (+1.0508131562507286, +0.51486991107242297), (+1.7623986880935312, +0.42167184787002709), (+1.0074316082553114, +0.51912205056097949), (+1.4112903123450415, +0.26185862712356989), (+1.4489864673792756, +0.40447112877686098), (+1.5828712984126319, +0.66991775577353663), (+1.1217428339671716, +0.28943207221088918), (+1.4477529693370408, +0.33580538151242889), (+1.2036324341274947, +0.91034481395774203), (+1.7674379319822398, +0.84169175112477213), (+1.0353493338604882, +0.79627526143505034), (+1.6638083356988855, +0.92008185257895081), (+1.5282001826750422, +0.85868668644110369), (+1.6338770247917767, +0.18198334347498257), (+1.4942299458838175, +0.99923805128752075), (+1.3654230189970751, +0.33789458599838484), (+1.6905056433431205, +0.71151407192741023), (+1.9841407237991875, +0.70021201624884966), (+1.4149168847274829, +0.74736103313343127E-2), (+1.7008006590375642, +0.80967555301256811), (+1.3856256409956140, +0.90700435010128655), (+1.8372597670169906, +0.60968682510709582), (+1.9402839807337642, +0.82403389304348151), (+1.5286532044195504, +0.80942850450471360), (+1.6257201208180729, +0.50921956330393969), (+1.5749924848936365, +0.59117651053321363), (+1.8320506529321872, +0.89626345641839900), (+1.5054971371851789, +0.84543895515168321), (+1.0526267910831071, +0.42490978784998468), (+1.0440713940267570, +0.53517929046086654), (+1.3990409090286984, +0.63691648924897315E-2), (+1.4885463551022249, +0.93557277976090891), (+1.9425579167631097, +0.84505049074774197), (+1.4418732877315570, +0.65479659689152070), (+1.0672466074838525, +0.60826841409855181), (+1.7018823863625889, +0.84462041653070807), (+1.7992042964113151, +0.69564995476753189), (+1.9756136141684606, +0.53883969752126082), (+1.6137461623798550, +0.34981192843200670), (+1.1507599815626426, +0.30907055680245210E-1), (+1.1232973843368994, +0.58221869859583109), (+1.7035512747025279, +0.26167945322008945E-1), (+1.2349134564185533, +0.93433186233891496), (+1.7399807534795402, +0.45723111374279179), (+1.0871617370362281, +0.89687404680241811), (+1.9051788705041590, +0.43976384567294502), (+1.3368168250448660, +0.98796408049177276), (+1.3117584553623889, +0.84783468449806365), (+1.5206705467386188, +0.74568508196552019), (+1.4515966452932321, +0.18477636674346376)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.7963104043559004, +0.10637082583187474), (+1.3069909152188870, +0.11836222327626172), (+1.8137206778307307, +0.65940581336449611), (+1.3110129993266235, +0.65040336286904088), (+1.9785225545125980, +0.78919912787531443), (+1.2690542392905348, +0.77966450369900731), (+1.5237971366481007, +0.64573457843489845), (+1.3280509241619289, +0.98220876961150694), (+1.7676089004834050, +0.50279080753382444E-1), (+1.3865365798091396, +0.82906989800056685), (+1.3060701071461231, +0.59584524086238511), (+1.5326350665249593, +0.46874638377425903), (+1.6245288016258550, +0.38157049243912666), (+1.0079837011915667, +0.30208203059722477), (+1.8539531626790382, +0.11082913353240337), (+1.4838454603576614, +0.70229485099907374), (+1.4107020464127000, +0.75393800781390530), (+1.1860888312137225, +0.88822744465302028), (+1.9456789446281544, +0.35288111988647314), (+1.2491143363315167, +0.43875506116692159), (+1.5717684971127128, +0.28205932044632454), (+1.6322904079047476, +0.17167445275799870), (+1.0131550590235272, +0.68449789793036342), (+1.4741874324919708, +0.42188376734337452), (+1.1946800324062128, +0.79913418573006745), (+1.9190926424822878, +0.35064826348427891E-1), (+1.8408845798681051, +0.94136770889401744), (+1.5145350195923220, +0.14128110595632773), (+1.9988769877153016, +0.42841927300002514), (+1.7960335650452381, +0.44922130423344564), (+1.3483263408664428, +0.15748171573241257), (+1.7228816993266376, +0.14183493641310005), (+1.8108421882871477, +0.95924609083743034E-1), (+1.2775908015251005, +0.38666190424747493), (+1.6219108123861925, +0.47646618116515038), (+1.6500750308521024, +0.91064757380676009), (+1.0508131562507290, +0.51486991107242286), (+1.7623986880935307, +0.42167184787002665), (+1.0074316082553114, +0.51912205056097926), (+1.4112903123450415, +0.26185862712356961), (+1.4489864673792754, +0.40447112877686087), (+1.5828712984126321, +0.66991775577353629), (+1.1217428339671716, +0.28943207221088907), (+1.4477529693370408, +0.33580538151242895), (+1.2036324341274951, +0.91034481395774169), (+1.7674379319822395, +0.84169175112477190), (+1.0353493338604882, +0.79627526143505034), (+1.6638083356988849, +0.92008185257895037), (+1.5282001826750427, +0.85868668644110346), (+1.6338770247917769, +0.18198334347498252), (+1.4942299458838173, +0.99923805128752030), (+1.3654230189970753, +0.33789458599838473), (+1.6905056433431205, +0.71151407192741001), (+1.9841407237991873, +0.70021201624884921), (+1.4149168847274827, +0.74736103313340352E-2), (+1.7008006590375637, +0.80967555301256788), (+1.3856256409956140, +0.90700435010128644), (+1.8372597670169903, +0.60968682510709560), (+1.9402839807337640, +0.82403389304348118), (+1.5286532044195504, +0.80942850450471338), (+1.6257201208180732, +0.50921956330393936), (+1.5749924848936367, +0.59117651053321318), (+1.8320506529321867, +0.89626345641839833), (+1.5054971371851786, +0.84543895515168266), (+1.0526267910831071, +0.42490978784998457), (+1.0440713940267570, +0.53517929046086654), (+1.3990409090286979, +0.63691648924892874E-2), (+1.4885463551022249, +0.93557277976090925), (+1.9425579167631097, +0.84505049074774174), (+1.4418732877315568, +0.65479659689152059), (+1.0672466074838522, +0.60826841409855148), (+1.7018823863625889, +0.84462041653070807), (+1.7992042964113149, +0.69564995476753211), (+1.9756136141684604, +0.53883969752126082), (+1.6137461623798548, +0.34981192843200659), (+1.1507599815626426, +0.30907055680245016E-1), (+1.1232973843368994, +0.58221869859583064), (+1.7035512747025277, +0.26167945322008890E-1), (+1.2349134564185531, +0.93433186233891430), (+1.7399807534795397, +0.45723111374279146), (+1.0871617370362281, +0.89687404680241789), (+1.9051788705041588, +0.43976384567294508), (+1.3368168250448660, +0.98796408049177220), (+1.3117584553623891, +0.84783468449806332), (+1.5206705467386188, +0.74568508196551975), (+1.4515966452932316, +0.18477636674346337), (+0.55511151231257827E-15, +0.0000000000000000), (+0.11102230246251565E-15, -0.47184478546569153E-15), (-0.22204460492503131E-15, +0.0000000000000000), (+0.0000000000000000, -0.22204460492503131E-15), (+0.11102230246251565E-15, -0.44408920985006262E-15), (+0.11102230246251565E-15, -0.47184478546569153E-15), (+0.44408920985006262E-15, -0.11102230246251565E-15), (+0.44408920985006262E-15, -0.36082248300317588E-15), (+0.44408920985006262E-15, +0.13877787807814457E-15), (+0.33306690738754696E-15, -0.24980018054066022E-15), (+0.0000000000000000, +0.24980018054066022E-15), (+0.11102230246251565E-15, -0.27755575615628914E-16), (-0.22204460492503131E-15, +0.41633363423443370E-15), (-0.11102230246251565E-15, -0.27755575615628914E-15), (+0.0000000000000000, +0.22204460492503131E-15), (-0.33306690738754696E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, +0.49960036108132044E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (-0.66613381477509392E-15, -0.83266726846886741E-16), (+0.22204460492503131E-15, +0.0000000000000000), (+0.11102230246251565E-15, +0.19428902930940239E-15), (+0.0000000000000000, -0.27755575615628914E-15), (+0.0000000000000000, +0.55511151231257827E-16), (+0.0000000000000000, +0.55511151231257827E-16), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.66613381477509392E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.13877787807814457E-15), (+0.0000000000000000, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.49960036108132044E-15), (+0.11102230246251565E-15, +0.72164496600635175E-15), (+0.11102230246251565E-15, +0.72164496600635175E-15), (+0.11102230246251565E-15, -0.22204460492503131E-15), (+0.44408920985006262E-15, +0.33306690738754696E-15), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.33306690738754696E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, +0.38857805861880479E-15), (+0.55511151231257827E-15, +0.61062266354383610E-15), (-0.11102230246251565E-15, +0.77715611723760958E-15), (+0.44408920985006262E-15, +0.55511151231257827E-15)

130reltol = sqrt(epsilon(1._TKC))

131reltol

132+0.14901161193847656E-7

133isClose(data, atad(1:size(data)), reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+7

140data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

141data

142(+1.09144970704576992490733911582168933, +0.542922096518878626242530617677452144), (+1.72045531456883377716347577039137885, +0.345439652592093095169179931877390480), (+1.33698992514390138496008752471751701, +0.299679681024032032100978368034106753), (+1.39055816969230064545272276855793391, +0.429824053972779522640937138564207424), (+1.49257668436633874486520528598519964, +0.661368194995671859231417679180847193), (+1.17101616805313515648116530703381025, +0.154249774415561783230196588624832220), (+1.17520693861439014208041569339678587, +0.280439996410977469864693393700455986)

143

144atad = getFFTI(getFFTF(data))

145atad

146(+1.09144970704576992490733911582168933, +0.542922096518878626242530617677452144), (+1.72045531456883377716347577039137904, +0.345439652592093095169179931877390480), (+1.33698992514390138496008752471751682, +0.299679681024032032100978368034106705), (+1.39055816969230064545272276855793411, +0.429824053972779522640937138564207327), (+1.49257668436633874486520528598519983, +0.661368194995671859231417679180847289), (+1.17101616805313515648116530703381045, +0.154249774415561783230196588624832172), (+1.17520693861439014208041569339678587, +0.280439996410977469864693393700455937), (+0.385185988877447170611195588516985464E-33, +0.722223729145213444895991728469347744E-34)

147reltol = sqrt(epsilon(1._TKC))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, atad(1:size(data)), reltol = reltol)

151T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+59

157data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

158data

159+1.64533114, +1.14040518, +1.41161716, +1.81318653, +1.35418034, +1.16278183, +1.71755695, +1.80859494, +1.18931270, +1.41320765, +1.80776417, +1.79708970, +1.54879189, +1.39269435, +1.73392808, +1.67295790, +1.24282324, +1.59888935, +1.14307547, +1.08644605, +1.24555433, +1.62103295, +1.48918843, +1.52175975, +1.48371696, +1.10096931, +1.52310884, +1.18113565, +1.45443583, +1.93724513, +1.39678764, +1.62640214, +1.71436524, +1.86166275, +1.90058136, +1.59374809, +1.62415504, +1.19992852, +1.26708913, +1.52099729, +1.12824440, +1.90369225, +1.95038891, +1.21293736, +1.99099994, +1.88021159, +1.25520968, +1.05258453, +1.96361959, +1.51338720, +1.22658038, +1.85359466, +1.10687208, +1.98767352, +1.59701633, +1.69436169, +1.10023952, +1.96265364, +1.67449772

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.64533114, +1.14040506, +1.41161704, +1.81318653, +1.35418022, +1.16278183, +1.71755672, +1.80859470, +1.18931282, +1.41320753, +1.80776393, +1.79708934, +1.54879189, +1.39269423, +1.73392797, +1.67295778, +1.24282324, +1.59888923, +1.14307547, +1.08644605, +1.24555445, +1.62103295, +1.48918831, +1.52175963, +1.48371696, +1.10096931, +1.52310872, +1.18113554, +1.45443559, +1.93724513, +1.39678764, +1.62640214, +1.71436524, +1.86166275, +1.90058136, +1.59374821, +1.62415516, +1.19992864, +1.26708913, +1.52099705, +1.12824452, +1.90369201, +1.95038879, +1.21293712, +1.99099970, +1.88021159, +1.25520968, +1.05258453, +1.96361959, +1.51338708, +1.22658038, +1.85359454, +1.10687208, +1.98767304, +1.59701622, +1.69436157, +1.10023975, +1.96265340, +1.67449760, +0.238418579E-6, +0.596046448E-7, -0.596046448E-7, +0.178813934E-6, +0.596046448E-7

164reltol = sqrt(epsilon(1._TKC))

165reltol

166+0.345266977E-3

167isClose(data, atad(1:size(data)), reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+40

174data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

175data

176+1.2059597546274099, +1.5186510062630409, +1.8394739814491714, +1.6459117447861000, +1.0148704614268276, +1.1515439380940808, +1.3145915997735638, +1.5945516317625683, +1.5618816012434245, +1.1687360762988606, +1.2545807546833312, +1.1969753020523113, +1.4681032528353630, +1.0593640318583599, +1.7437533510153544, +1.0113203084282638, +1.0171292437987687, +1.6671720515381012, +1.4625301753014148, +1.8292008409334870, +1.9076254466099689, +1.2678201627855450, +1.0951219064899951, +1.4574489000298025, +1.4307450005407769, +1.6803212772654144, +1.8438311414977147, +1.1485184064761842, +1.5317702377848752, +1.8604864531951240, +1.7549381685266161, +1.8378750131682398, +1.2291618249460048, +1.5738320319704462, +1.6595868680397325, +1.5760843392639892, +1.6331369493941266, +1.9968378975737697, +1.0226105671138657, +1.3140534626888638

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.2059597546274097, +1.5186510062630412, +1.8394739814491714, +1.6459117447861009, +1.0148704614268271, +1.1515439380940813, +1.3145915997735635, +1.5945516317625685, +1.5618816012434240, +1.1687360762988606, +1.2545807546833305, +1.1969753020523113, +1.4681032528353621, +1.0593640318583599, +1.7437533510153536, +1.0113203084282638, +1.0171292437987685, +1.6671720515381014, +1.4625301753014144, +1.8292008409334868, +1.9076254466099680, +1.2678201627855450, +1.0951219064899946, +1.4574489000298021, +1.4307450005407767, +1.6803212772654141, +1.8438311414977140, +1.1485184064761835, +1.5317702377848743, +1.8604864531951235, +1.7549381685266157, +1.8378750131682393, +1.2291618249460050, +1.5738320319704464, +1.6595868680397328, +1.5760843392639889, +1.6331369493941263, +1.9968378975737697, +1.0226105671138661, +1.3140534626888636, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.88817841970012523E-15, -0.33306690738754696E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.77715611723760958E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.88817841970012523E-15, +0.66613381477509392E-15, +0.55511151231257827E-15, +0.88817841970012523E-15, +0.22204460492503131E-15, +0.88817841970012523E-15

181reltol = sqrt(epsilon(1._TKC))

182reltol

183+0.14901161193847656E-7

184isClose(data, atad(1:size(data)), reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+82

191data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

192data

193+1.86372636803108595390913170110723164, +1.25522406665145710234963693450151928, +1.74987571328290404884398233036561909, +1.07653516746709600549175631548212131, +1.23878739286081557013348649512772949, +1.65144967372479654150789245949676796, +1.70295517582884848304912063487603242, +1.69275703206682195560293799995016540, +1.79890100878747743934143638767794895, +1.63055483711489732168273672644798892, +1.35794519451258637075218705259955360, +1.57956248886040443013580179571816540, +1.03892200144251362102289424901441369, +1.16268353100646584735337402275866737, +1.22126896082934887661553280641262483, +1.89203564601941965562116028372617537, +1.01433489084708199162240736412253978, +1.11076684187622567475298293214190858, +1.24498654286666633305496662971449658, +1.49778002992200233776642677607092691, +1.76240436334309348378926599420183903, +1.61827418692074429333105857605739718, +1.90815450275993058993854678341430505, +1.12293137039034468585680198646996284, +1.78664855798586040282233436966645516, +1.44030309700246544912595110924720420, +1.93460303040926330095261871406397828, +1.85124568259555861990191737018881272, +1.00366408821673797845378256317190912, +1.00969141049334699226832911614387640, +1.91948463549473219442233598244908011, +1.43807111810835605894280172335142729, +1.56003054238045873800309555989360560, +1.23887010692857316486291901981561475, +1.13119386014964719915967035384600374, +1.34739025135391712562582207861175183, +1.57627713131126139468257597493770197, +1.84618815053239814534535878996680206, +1.39033436671397837769271173150718659, +1.04714767606756092040999524229373910, +1.96655495444772621911815602071081324, +1.93803050129688482698911010785077631, +1.68423445755329894347641794244361531, +1.62144008467128165398762277257093963, +1.54576965300506973259528849628520095, +1.86151299396628264568143742204334279, +1.43997749254615312506481445367816690, +1.36814561382178850255695500498335317, +1.11237680546865324321435327084548774, +1.86878274045685686966635521223024536, +1.75050190156764866565484891554906271, +1.74155277999746609128796006922279783, +1.32865941598578288723602125605770438, +1.31782678770145682916105727533418639, +1.07008900042592859090216718689735491, +1.98026742447657527434171939787125151, +1.83451819194420707559686521422256488, +1.02018383949979030463148835145454878, +1.35584993502109397118138706764277467, +1.56235724410949876764512253857909821, +1.34509766364961051946576591928823975, +1.87229295220502206055347325008593484, +1.55207698515286299735274681327603686, +1.01242315874361305674496955168948032, +1.99315992622103709908527783991098383, +1.32949044886404348873634315575938514, +1.19125742666569058070440769757899800, +1.55962098799111132542144999391586401, +1.54606813790857197347209495118914462, +1.63237172179708436919516347411322941, +1.37402992264519417304612550896858663, +1.04387922291756081547419875374882047, +1.78763501171787169198495549986308880, +1.42043855316463369685149165300926739, +1.34022167206876433330813932265173593, +1.57515719988510550347362564226455512, +1.17861033788031975697259613924918298, +1.16968704332163524345032945627948934, +1.73219384119463447593471276574136663, +1.83237239661485725617782733548101375, +1.97377992056475955617867302748739986, +1.54103407578638915156448515991901002

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.86372636803108595390913170110723164, +1.25522406665145710234963693450151947, +1.74987571328290404884398233036561929, +1.07653516746709600549175631548212151, +1.23878739286081557013348649512772969, +1.65144967372479654150789245949676815, +1.70295517582884848304912063487603222, +1.69275703206682195560293799995016560, +1.79890100878747743934143638767794914, +1.63055483711489732168273672644798892, +1.35794519451258637075218705259955380, +1.57956248886040443013580179571816560, +1.03892200144251362102289424901441407, +1.16268353100646584735337402275866737, +1.22126896082934887661553280641262502, +1.89203564601941965562116028372617576, +1.01433489084708199162240736412253940, +1.11076684187622567475298293214190839, +1.24498654286666633305496662971449639, +1.49778002992200233776642677607092729, +1.76240436334309348378926599420183884, +1.61827418692074429333105857605739718, +1.90815450275993058993854678341430467, +1.12293137039034468585680198646996304, +1.78664855798586040282233436966645516, +1.44030309700246544912595110924720420, +1.93460303040926330095261871406397828, +1.85124568259555861990191737018881349, +1.00366408821673797845378256317190874, +1.00969141049334699226832911614387659, +1.91948463549473219442233598244907953, +1.43807111810835605894280172335142729, +1.56003054238045873800309555989360522, +1.23887010692857316486291901981561475, +1.13119386014964719915967035384600374, +1.34739025135391712562582207861175183, +1.57627713131126139468257597493770177, +1.84618815053239814534535878996680187, +1.39033436671397837769271173150718639, +1.04714767606756092040999524229373852, +1.96655495444772621911815602071081343, +1.93803050129688482698911010785077650, +1.68423445755329894347641794244361551, +1.62144008467128165398762277257093982, +1.54576965300506973259528849628520152, +1.86151299396628264568143742204334279, +1.43997749254615312506481445367816710, +1.36814561382178850255695500498335297, +1.11237680546865324321435327084548735, +1.86878274045685686966635521223024536, +1.75050190156764866565484891554906271, +1.74155277999746609128796006922279763, +1.32865941598578288723602125605770476, +1.31782678770145682916105727533418601, +1.07008900042592859090216718689735491, +1.98026742447657527434171939787125093, +1.83451819194420707559686521422256450, +1.02018383949979030463148835145454839, +1.35584993502109397118138706764277447, +1.56235724410949876764512253857909802, +1.34509766364961051946576591928823994, +1.87229295220502206055347325008593464, +1.55207698515286299735274681327603705, +1.01242315874361305674496955168947917, +1.99315992622103709908527783991098364, +1.32949044886404348873634315575938514, +1.19125742666569058070440769757899819, +1.55962098799111132542144999391586382, +1.54606813790857197347209495118914500, +1.63237172179708436919516347411322922, +1.37402992264519417304612550896858663, +1.04387922291756081547419875374882028, +1.78763501171787169198495549986308841, +1.42043855316463369685149165300926777, +1.34022167206876433330813932265173555, +1.57515719988510550347362564226455531, +1.17861033788031975697259613924918336, +1.16968704332163524345032945627948934, +1.73219384119463447593471276574136721, +1.83237239661485725617782733548101394, +1.97377992056475955617867302748739967, +1.54103407578638915156448515991901002, +0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, +0.577778983316170755916793382775478196E-33, -0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-33, -0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, +0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000

198reltol = sqrt(epsilon(1._TKC))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, atad(1:size(data)), reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+24

208data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

209data

210(+1.96766543, +0.710063875), (+1.11891305, +0.326115131), (+1.31668377, +0.872716010), (+1.32098162, +0.891863525), (+1.15434742, +0.157239199), (+1.89377141, +0.330090880), (+1.82859015, +0.991395831), (+1.47945333, +0.502094626), (+1.06136513, +0.207013369), (+1.66409111, +0.764193118), (+1.56416488, +0.463738739), (+1.40158463, +0.110465407), (+1.53070414, +0.115062952), (+1.30377829, +0.437621355), (+1.41426909, +0.666747451), (+1.35315275, +0.181444943), (+1.79727435, +0.889222145), (+1.81917310, +0.233229101), (+1.36905289, +0.641065836E-2), (+1.60844171, +0.862709582), (+1.14533472, +0.489053011), (+1.79820895, +0.709334850), (+1.16092968, +0.200106919), (+1.02968466, +0.412979245)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.96766543, +0.710063934), (+1.11891282, +0.326115072), (+1.31668401, +0.872716010), (+1.32098150, +0.891863525), (+1.15434742, +0.157239228), (+1.89377129, +0.330090821), (+1.82858992, +0.991395772), (+1.47945344, +0.502094746), (+1.06136513, +0.207013369), (+1.66409111, +0.764193177), (+1.56416488, +0.463738710), (+1.40158451, +0.110465556), (+1.53070414, +0.115062982), (+1.30377805, +0.437621474), (+1.41426897, +0.666747451), (+1.35315263, +0.181445062), (+1.79727435, +0.889222145), (+1.81917274, +0.233229086), (+1.36905313, +0.641077757E-2), (+1.60844159, +0.862709582), (+1.14533472, +0.489052922), (+1.79820883, +0.709334671), (+1.16092992, +0.200106919), (+1.02968466, +0.412979215), (+0.00000000, +0.745058060E-8), (-0.596046448E-7, +0.119209290E-6), (+0.298023224E-6, -0.298023224E-7), (-0.119209290E-6, -0.298023224E-7), (+0.119209290E-6, +0.298023224E-7), (-0.119209290E-6, +0.119209290E-6), (+0.178813934E-6, -0.298023224E-7), (-0.119209290E-6, -0.596046448E-7)

215reltol = sqrt(epsilon(1._TKC))

216reltol

217+0.345266977E-3

218isClose(data, atad(1:size(data)), reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+58

225data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

226data

227(+1.8695281605179637, +0.39396317604940512), (+1.4435688369502531, +0.46223847818042452E-1), (+1.5420873924531431, +0.40369023337278753), (+1.8315999911801719, +0.56274418844181329), (+1.1885459959457609, +0.62094468300152306E-2), (+1.0189727842075151, +0.97134518210244392), (+1.0026263573830154, +0.74862287460848909), (+1.5129466052155700, +0.21234641577703162), (+1.6934308555287927, +0.11647133021736400), (+1.2644929606277480, +0.96955277390034345), (+1.6930526416153548, +0.47342509144996459), (+1.2399400116894688, +0.31220251290535705), (+1.5507818974420005, +0.76130902996911587), (+1.5382134008053225, +0.33311879731111493E-1), (+1.5362524527106778, +0.96945779261905896), (+1.4748049496433455, +0.31997923992976629), (+1.2928790212830608, +0.86575251140989240), (+1.3506696712426716, +0.73429460028192683), (+1.2973180651022416, +0.35674206178877865), (+1.5252679452498747, +0.74871960337951560), (+1.6753888416357017, +0.71467495868948205), (+1.7359400871396287, +0.97614176954910326), (+1.5827135351905823, +0.34468480836993864), (+1.5549257071794451, +0.72863741910212143), (+1.7270506520170743, +0.32220495140752436), (+1.9921909954182362, +0.22377786666645116), (+1.9765007946271065, +0.26503623848944369), (+1.1734071692449912, +0.77687342349381316), (+1.3237002579238633, +0.98231995011927598), (+1.7763624107425826, +0.19912537921721352), (+1.6407224484428136, +0.54969258310331570), (+1.1786180072855719, +0.15350640433072971), (+1.9386552602333316, +0.41426856394069422), (+1.0068273112311108, +0.67167577937460310E-1), (+1.6732975563114114, +0.81596884694565752), (+1.3162547509015672, +0.12637696497301754), (+1.6647448594384957, +0.43634939861611965), (+1.7674947599935729, +0.57948232884740403), (+1.9183775613947143, +0.28158645795687276), (+1.3500426330930559, +0.32767139570520643), (+1.2548038217998683, +0.74581025707489479E-1), (+1.2279544612479705, +0.54639856557627853), (+1.8843511820995875, +0.77735905793264071), (+1.5210839694196068, +0.52207663903055657), (+1.0806346415598176, +0.45730300706763172), (+1.7979326701369784, +0.67751297408322142), (+1.7065496953680797, +0.30911441020019637), (+1.6399120431889740, +0.60045008209484818), (+1.9071300801852131, +0.16262851820245372), (+1.4505754657824310, +0.59339626329043427), (+1.4173058701011740, +0.34378672059241921), (+1.9699084043462201, +0.72380195582708029), (+1.2395906427681114, +0.89245748256375768E-2), (+1.9729697289331967, +0.17570781729168994), (+1.9622927181352681, +0.60238185661102761), (+1.4451018820009174, +0.64822654353167253E-1), (+1.6780143220774892, +0.93505545340572971), (+1.7222594079896163, +0.48633509746108217)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.8695281605179639, +0.39396317604940512), (+1.4435688369502531, +0.46223847818042632E-1), (+1.5420873924531429, +0.40369023337278759), (+1.8315999911801717, +0.56274418844181362), (+1.1885459959457612, +0.62094468300152861E-2), (+1.0189727842075149, +0.97134518210244369), (+1.0026263573830156, +0.74862287460848909), (+1.5129466052155705, +0.21234641577703151), (+1.6934308555287931, +0.11647133021736418), (+1.2644929606277484, +0.96955277390034345), (+1.6930526416153548, +0.47342509144996453), (+1.2399400116894688, +0.31220251290535717), (+1.5507818974420005, +0.76130902996911620), (+1.5382134008053230, +0.33311879731111660E-1), (+1.5362524527106778, +0.96945779261905896), (+1.4748049496433460, +0.31997923992976651), (+1.2928790212830610, +0.86575251140989240), (+1.3506696712426716, +0.73429460028192706), (+1.2973180651022416, +0.35674206178877854), (+1.5252679452498752, +0.74871960337951549), (+1.6753888416357017, +0.71467495868948216), (+1.7359400871396291, +0.97614176954910326), (+1.5827135351905826, +0.34468480836993892), (+1.5549257071794456, +0.72863741910212121), (+1.7270506520170747, +0.32220495140752403), (+1.9921909954182362, +0.22377786666645122), (+1.9765007946271065, +0.26503623848944369), (+1.1734071692449919, +0.77687342349381305), (+1.3237002579238633, +0.98231995011927553), (+1.7763624107425831, +0.19912537921721346), (+1.6407224484428138, +0.54969258310331537), (+1.1786180072855723, +0.15350640433072976), (+1.9386552602333318, +0.41426856394069411), (+1.0068273112311110, +0.67167577937460352E-1), (+1.6732975563114114, +0.81596884694565741), (+1.3162547509015672, +0.12637696497301754), (+1.6647448594384959, +0.43634939861611971), (+1.7674947599935733, +0.57948232884740403), (+1.9183775613947145, +0.28158645795687276), (+1.3500426330930564, +0.32767139570520643), (+1.2548038217998687, +0.74581025707489632E-1), (+1.2279544612479711, +0.54639856557627831), (+1.8843511820995871, +0.77735905793264015), (+1.5210839694196068, +0.52207663903055634), (+1.0806346415598176, +0.45730300706763172), (+1.7979326701369782, +0.67751297408322131), (+1.7065496953680797, +0.30911441020019603), (+1.6399120431889740, +0.60045008209484785), (+1.9071300801852133, +0.16262851820245372), (+1.4505754657824310, +0.59339626329043416), (+1.4173058701011740, +0.34378672059241910), (+1.9699084043462207, +0.72380195582708018), (+1.2395906427681112, +0.89245748256374657E-2), (+1.9729697289331969, +0.17570781729168988), (+1.9622927181352683, +0.60238185661102706), (+1.4451018820009178, +0.64822654353166975E-1), (+1.6780143220774897, +0.93505545340572960), (+1.7222594079896161, +0.48633509746108222), (+0.66613381477509392E-15, +0.27755575615628914E-16), (+0.44408920985006262E-15, -0.27755575615628914E-15), (+0.55511151231257827E-15, +0.33306690738754696E-15), (+0.66613381477509392E-15, -0.33306690738754696E-15), (+0.88817841970012523E-15, +0.55511151231257827E-15), (+0.11102230246251565E-14, +0.26367796834847468E-15)

232reltol = sqrt(epsilon(1._TKC))

233reltol

234+0.14901161193847656E-7

235isClose(data, atad(1:size(data)), reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+24

242data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

243data

244(+1.34893993906315543041619320826502066, +0.839827272130403374849170346350256722), (+1.92272262449539690778468530048575507, +0.669655490003550720114092664813413213), (+1.52861631942928043112756024911316244, +0.147924934569875451341053492089545824), (+1.40135792994441591431799700706688318, +0.836149854152803305450815193261315692), (+1.88766738339644999836680421034227237, +0.676556216498769805727507529601454925), (+1.89358654368497111457450982823937193, +0.199194133492887641123564999598072346), (+1.43622879228912193940333408996389247, +0.126554344138623716771860439600128389E-1), (+1.13206575815482069327389717436414644, +0.362801156833665839228516099035409352), (+1.25325824594670074561454204356584365, +0.420201050316842695747329725710098652), (+1.54470257354413215309846725286661266, +0.224344277147475640037543028340179666), (+1.96541565786585456918394315055240739, +0.554875848065008173411187963587471683), (+1.92463712083111573719507378962379313, +0.987531790586124459596658138970958449), (+1.38342586067946074438472676075169745, +0.250705049983560360083845168205044440), (+1.98484490183529190298006753175677272, +0.842258380959566094743319255167505252), (+1.44168771245058760076655254454947223, +0.476530121193697668095346017438931113), (+1.05778636900449900713365906088580180, +0.121922343432951182095316916532130048), (+1.31081616491326415475314192246453420, +0.575671153336177524509906522197052824), (+1.11715699363276571929669047732370367, +0.924039015234662184020302046703482261), (+1.09280575791181910048670636207588273, +0.236204270834545406748961739162614319), (+1.52972505932285487978449820749683638, +0.771177426592665776805511325336210528), (+1.60670473468670027025081491920387479, +0.629290256716113437009104483335964955), (+1.76080580162578489358707672954394914, +0.320406488833168388027360822284970364), (+1.70768829122884523026822202331092995, +0.384553940588981519436076977593861983), (+1.73237235351180053486062254123867917, +0.912284363552888856817637833373896542)

245

246atad = getFFTI(getFFTF(data))

247atad

248(+1.34893993906315543041619320826502047, +0.839827272130403374849170346350256722), (+1.92272262449539690778468530048575488, +0.669655490003550720114092664813413309), (+1.52861631942928043112756024911316263, +0.147924934569875451341053492089545751), (+1.40135792994441591431799700706688318, +0.836149854152803305450815193261315789), (+1.88766738339644999836680421034227217, +0.676556216498769805727507529601454925), (+1.89358654368497111457450982823937193, +0.199194133492887641123564999598072249), (+1.43622879228912193940333408996389266, +0.126554344138623716771860439600125982E-1), (+1.13206575815482069327389717436414682, +0.362801156833665839228516099035409160), (+1.25325824594670074561454204356584384, +0.420201050316842695747329725710098652), (+1.54470257354413215309846725286661247, +0.224344277147475640037543028340179594), (+1.96541565786585456918394315055240739, +0.554875848065008173411187963587471876), (+1.92463712083111573719507378962379313, +0.987531790586124459596658138970958449), (+1.38342586067946074438472676075169745, +0.250705049983560360083845168205044489), (+1.98484490183529190298006753175677272, +0.842258380959566094743319255167505252), (+1.44168771245058760076655254454947223, +0.476530121193697668095346017438931402), (+1.05778636900449900713365906088580142, +0.121922343432951182095316916532130072), (+1.31081616491326415475314192246453420, +0.575671153336177524509906522197052631), (+1.11715699363276571929669047732370367, +0.924039015234662184020302046703482453), (+1.09280575791181910048670636207588254, +0.236204270834545406748961739162614392), (+1.52972505932285487978449820749683638, +0.771177426592665776805511325336210625), (+1.60670473468670027025081491920387460, +0.629290256716113437009104483335965147), (+1.76080580162578489358707672954394934, +0.320406488833168388027360822284970460), (+1.70768829122884523026822202331093015, +0.384553940588981519436076977593862031), (+1.73237235351180053486062254123867975, +0.912284363552888856817637833373896542), (+0.962964972193617926527988971292463659E-34, +0.722223729145213444895991728469347744E-34), (+0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (+0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34), (+0.962964972193617926527988971292463659E-34, -0.722223729145213444895991728469347744E-34), (-0.962964972193617926527988971292463659E-34, +0.168518870133883137142398069976181140E-33)

249reltol = sqrt(epsilon(1._TKC))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, atad(1:size(data)), reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+20

259data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

260data

261+1.33541369, +1.79310298, +1.69072664, +1.39497304, +1.48348618, +1.77758551, +1.91302061, +1.25841379, +1.26356363, +1.62864923, +1.57108784, +1.87743819, +1.10393775, +1.70560169, +1.46695161, +1.31761098, +1.29751897, +1.56798434, +1.41365862, +1.58063710

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.33541369, +1.79310298, +1.69072676, +1.39497316, +1.48348594, +1.77758527, +1.91302037, +1.25841391, +1.26356375, +1.62864912, +1.57108796, +1.87743807, +1.10393798, +1.70560145, +1.46695185, +1.31761062, +1.29751897, +1.56798434, +1.41365862, +1.58063710, -0.596046448E-7, +0.596046448E-7, +0.178813934E-6, -0.119209290E-6, -0.238418579E-6, +0.119209290E-6, -0.119209290E-6, +0.00000000, -0.119209290E-6, +0.596046448E-7, +0.596046448E-7, +0.357627869E-6

266reltol = sqrt(epsilon(1._TKC))

267reltol

268+0.345266977E-3

269isClose(data, atad(1:size(data)), reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+97

276data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

277data

278+1.3634260317878550, +1.3787322819596646, +1.7835879535731669, +1.2375483787225057, +1.1774000688745885, +1.8439753823985043, +1.0285472747107920, +1.9970007171051618, +1.8852651137512737, +1.2382163321999422, +1.0569874904301519, +1.4839414812074758, +1.4021165554855721, +1.9749376740722422, +1.6108797310690690, +1.2284260609594391, +1.4641610232498274, +1.3050945419700977, +1.7097136505207140, +1.4991198043513205, +1.7374861159398551, +1.3417406328298425, +1.1232943726261007, +1.4182751720170375, +1.7582856192721867, +1.6614747581861271, +1.4923929197802632, +1.2945794080731330, +1.1417164865105873, +1.2768892597478305, +1.6282522805575921, +1.6428919335678227, +1.8036268633943520, +1.0034312905029046, +1.6104835864202038, +1.3478284689374163, +1.4099331518352598, +1.7684947457221678, +1.3047752301563258, +1.1381897330521380, +1.5974486349294081, +1.1333610566499428, +1.5672831719111078, +1.7451127133390578, +1.4934099185313152, +1.4686289754318571, +1.9882974553453627, +1.5064308965184559, +1.6495821395159154, +1.6877574659140655, +1.0378560129067744, +1.3483530056467414, +1.8928021636211034, +1.1555456920362639, +1.7514333395327935, +1.3643297793651947, +1.4113259295927669, +1.0525887372150959, +1.6822145185261856, +1.3109898258349371, +1.6887019922203965, +1.8130669837723898, +1.6357557809838870, +1.0333581629846242, +1.1828049827634990, +1.7718110502806916, +1.4077420228475079, +1.0093715945576636, +1.6581980137145802, +1.4688603599972532, +1.9748917459863291, +1.2317781257046247, +1.6913786443961478, +1.9236393985088034, +1.2526876536283049, +1.3633048034223745, +1.2062783135746469, +1.3171820621885604, +1.3292756900261451, +1.3740026386715996, +1.6780382672685654, +1.5043629011152451, +1.9771535213921210, +1.0275683297524516, +1.2822707976376391, +1.0549624184687705, +1.4418409959090335, +1.9628948628873024, +1.7015307403559159, +1.7072635187993344, +1.5539673015967059, +1.0279178566620275, +1.4709797174054533, +1.2294924476346583, +1.7607108125360975, +1.8258743208202834, +1.0975002391266093

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.3634260317878553, +1.3787322819596644, +1.7835879535731667, +1.2375483787225059, +1.1774000688745878, +1.8439753823985046, +1.0285472747107920, +1.9970007171051620, +1.8852651137512744, +1.2382163321999426, +1.0569874904301517, +1.4839414812074760, +1.4021165554855723, +1.9749376740722424, +1.6108797310690692, +1.2284260609594395, +1.4641610232498277, +1.3050945419700983, +1.7097136505207140, +1.4991198043513205, +1.7374861159398549, +1.3417406328298427, +1.1232943726261004, +1.4182751720170375, +1.7582856192721867, +1.6614747581861273, +1.4923929197802628, +1.2945794080731332, +1.1417164865105873, +1.2768892597478310, +1.6282522805575916, +1.6428919335678227, +1.8036268633943526, +1.0034312905029044, +1.6104835864202043, +1.3478284689374158, +1.4099331518352600, +1.7684947457221676, +1.3047752301563262, +1.1381897330521382, +1.5974486349294086, +1.1333610566499432, +1.5672831719111073, +1.7451127133390578, +1.4934099185313154, +1.4686289754318569, +1.9882974553453630, +1.5064308965184554, +1.6495821395159158, +1.6877574659140659, +1.0378560129067744, +1.3483530056467412, +1.8928021636211032, +1.1555456920362634, +1.7514333395327935, +1.3643297793651943, +1.4113259295927678, +1.0525887372150962, +1.6822145185261852, +1.3109898258349366, +1.6887019922203970, +1.8130669837723890, +1.6357557809838874, +1.0333581629846242, +1.1828049827634992, +1.7718110502806916, +1.4077420228475079, +1.0093715945576636, +1.6581980137145802, +1.4688603599972530, +1.9748917459863291, +1.2317781257046245, +1.6913786443961480, +1.9236393985088038, +1.2526876536283045, +1.3633048034223745, +1.2062783135746475, +1.3171820621885602, +1.3292756900261453, +1.3740026386715991, +1.6780382672685659, +1.5043629011152453, +1.9771535213921205, +1.0275683297524516, +1.2822707976376393, +1.0549624184687703, +1.4418409959090333, +1.9628948628873015, +1.7015307403559157, +1.7072635187993344, +1.5539673015967055, +1.0279178566620271, +1.4709797174054537, +1.2294924476346578, +1.7607108125360975, +1.8258743208202821, +1.0975002391266095, +0.0000000000000000, -0.11102230246251565E-15, -0.55511151231257827E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, -0.33306690738754696E-15, -0.33306690738754696E-15, -0.33306690738754696E-15, -0.55511151231257827E-15, +0.44408920985006262E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.22204460492503131E-15, +0.77715611723760958E-15, +0.77715611723760958E-15, +0.11102230246251565E-15, +0.66613381477509392E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.77715611723760958E-15, +0.99920072216264089E-15, +0.44408920985006262E-15

283reltol = sqrt(epsilon(1._TKC))

284reltol

285+0.14901161193847656E-7

286isClose(data, atad(1:size(data)), reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+50

293data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

294data

295+1.52757409304887876624493610700529611, +1.82011143928365464966672444844592076, +1.26064381039652730380205092035833293, +1.85146013858070811485771099964782387, +1.84584573852692442225128939159849476, +1.48935777872236390723476843699386356, +1.03191134654604574550561234335582937, +1.05113049451426208590963041063592379, +1.58511684184381989892759033117622648, +1.36283110401820783191659725426583796, +1.30633799809492113506150648836964175, +1.30899487432201853299389305237768085, +1.42703450061468277981708662178831826, +1.12715441520725364866814218843225857, +1.17623487549668616159592188104713518, +1.30811656874882297076713315383001738, +1.87090653924217871153378562568773680, +1.10961318097251174547010481669012048, +1.55066479736328230167159310967123563, +1.45417583967960856699996241958625122, +1.42344007078747547878221958879117150, +1.11486432575446092523176241003302075, +1.21515025753743529490248114245798459, +1.50755824163517967727139713790033340, +1.04137263573120445101670494501299204, +1.46850055074098033421506444181553813, +1.15913182641755116741403542865524931, +1.76304819210462647451506373230379850, +1.77217556947525120719442556378408360, +1.24001079158390333905331735165659750, +1.30278644837137310312293074603174124, +1.26028489808277077146429532421894629, +1.66795892934454050088587316596019082, +1.31053494190777286285870776213822707, +1.19687448389700752289161247061316786, +1.90672607910149219717094938431166830, +1.53200313277301705410011644919638359, +1.27743850886278308715144895058559184, +1.71105960280913489115385447543596848, +1.78271214266597108229181166737997664, +1.73945391229701665866050648650274794, +1.73710137635922132497885697686461505, +1.52849128975869538993443587856161046, +1.63626417514618894946080741918910774, +1.60281895853473895708181402290707996, +1.26803795245398335106697019687978023, +1.06701686736588337386891149699154272, +1.58867364456672640250781389793529497, +1.49763169590057342753971256791498059, +1.21637747541754708714238965355754398

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.52757409304887876624493610700529631, +1.82011143928365464966672444844592114, +1.26064381039652730380205092035833274, +1.85146013858070811485771099964782387, +1.84584573852692442225128939159849495, +1.48935777872236390723476843699386394, +1.03191134654604574550561234335582976, +1.05113049451426208590963041063592359, +1.58511684184381989892759033117622686, +1.36283110401820783191659725426583853, +1.30633799809492113506150648836964195, +1.30899487432201853299389305237768104, +1.42703450061468277981708662178831845, +1.12715441520725364866814218843225896, +1.17623487549668616159592188104713557, +1.30811656874882297076713315383001719, +1.87090653924217871153378562568773680, +1.10961318097251174547010481669012068, +1.55066479736328230167159310967123524, +1.45417583967960856699996241958625102, +1.42344007078747547878221958879117150, +1.11486432575446092523176241003302113, +1.21515025753743529490248114245798459, +1.50755824163517967727139713790033302, +1.04137263573120445101670494501299204, +1.46850055074098033421506444181553852, +1.15913182641755116741403542865524950, +1.76304819210462647451506373230379792, +1.77217556947525120719442556378408379, +1.24001079158390333905331735165659788, +1.30278644837137310312293074603174143, +1.26028489808277077146429532421894591, +1.66795892934454050088587316596019121, +1.31053494190777286285870776213822707, +1.19687448389700752289161247061316805, +1.90672607910149219717094938431166811, +1.53200313277301705410011644919638359, +1.27743850886278308715144895058559223, +1.71105960280913489115385447543596867, +1.78271214266597108229181166737997703, +1.73945391229701665866050648650274813, +1.73710137635922132497885697686461563, +1.52849128975869538993443587856161085, +1.63626417514618894946080741918910774, +1.60281895853473895708181402290708016, +1.26803795245398335106697019687978061, +1.06701686736588337386891149699154310, +1.58867364456672640250781389793529536, +1.49763169590057342753971256791498079, +1.21637747541754708714238965355754418, +0.481482486096808963263994485646231830E-33, +0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-33, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33

300reltol = sqrt(epsilon(1._TKC))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, atad(1:size(data)), reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+92

310data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

311data

312(+1.57735014, +0.827689052), (+1.84340787, +0.328918636), (+1.86816669, +0.225601017), (+1.31747901, +0.772177517), (+1.55536139, +0.634938121), (+1.73754001, +0.109116137), (+1.13362432, +0.788132012), (+1.59592295, +0.175415695), (+1.15387392, +0.569356799), (+1.99453282, +0.337054133E-1), (+1.15021563, +0.313952208), (+1.96426785, +0.560929239), (+1.96859932, +0.345974922), (+1.33799386, +0.386271179), (+1.81126523, +0.144062400), (+1.26855922, +0.908781946), (+1.34850359, +0.239327550), (+1.54451466, +0.838136077), (+1.07100272, +0.747236073), (+1.09517026, +0.684722960), (+1.27919960, +0.987547696), (+1.56138563, +0.417937219), (+1.82110119, +0.271674871), (+1.87753582, +0.923350036), (+1.25692809, +0.399388790), (+1.92362189, +0.877989829), (+1.47921777, +0.768718958), (+1.40711033, +0.439919353), (+1.48806453, +0.566953063), (+1.92320096, +0.269255757), (+1.68985081, +0.348689675), (+1.86898053, +0.103491724), (+1.15623641, +0.192841053), (+1.97426629, +0.243214667), (+1.34635329, +0.512811780), (+1.96872306, +0.687351465), (+1.12904978, +0.190056860), (+1.54338276, +0.843733490), (+1.87741494, +0.781754255), (+1.58612108, +0.924536645), (+1.59401774, +0.305514395), (+1.61335826, +0.951383889), (+1.36662984, +0.653753459), (+1.51939464, +0.304568768), (+1.60781705, +0.392411470), (+1.72869909, +0.494312525), (+1.56681275, +0.199020982), (+1.98877382, +0.764280319), (+1.38840616, +0.168674529), (+1.01917076, +0.712672770), (+1.30150795, +0.631850660), (+1.89562941, +0.874550521), (+1.74518633, +0.769829094), (+1.30930412, +0.132590950), (+1.32012689, +0.814105988), (+1.50213277, +0.244354367), (+1.06989288, +0.272728980), (+1.24146175, +0.611429036), (+1.51787066, +0.308743000), (+1.62279654, +0.330386341), (+1.54465747, +0.356355786), (+1.24692285, +0.904499471), (+1.84842777, +0.522753179), (+1.32894540, +0.639031231), (+1.90354359, +0.578615665), (+1.10572553, +0.150998831), (+1.19408298, +0.279882789), (+1.81823564, +0.633821011), (+1.66833878, +0.226875901), (+1.99200714, +0.335895121), (+1.70004177, +0.236870646E-1), (+1.69536173, +0.854159951), (+1.71382976, +0.825032413), (+1.37814224, +0.423573554), (+1.69239450, +0.487397015), (+1.33342791, +0.261447072), (+1.74726880, +0.917255282E-1), (+1.42477632, +0.302263200), (+1.66209602, +0.705818415), (+1.27793396, +0.647675216), (+1.32098651, +0.776716650), (+1.30240226, +0.891858339E-2), (+1.06791580, +0.747151673), (+1.64405787, +0.208811879), (+1.04311836, +0.608524382), (+1.79520583, +0.204218805), (+1.73364425, +0.956647575), (+1.51841640, +0.342005432), (+1.31871462, +0.185924947), (+1.73752832, +0.107100010E-1), (+1.69234931, +0.110917270), (+1.23210645, +0.496393621)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.57735002, +0.827689052), (+1.84340811, +0.328918815), (+1.86816645, +0.225601047), (+1.31747890, +0.772177458), (+1.55536103, +0.634938002), (+1.73753977, +0.109116092), (+1.13362408, +0.788131952), (+1.59592271, +0.175415516), (+1.15387404, +0.569356740), (+1.99453306, +0.337056518E-1), (+1.15021574, +0.313952297), (+1.96426773, +0.560929179), (+1.96859932, +0.345974982), (+1.33799386, +0.386271268), (+1.81126511, +0.144062519), (+1.26855934, +0.908781767), (+1.34850359, +0.239327610), (+1.54451466, +0.838136137), (+1.07100260, +0.747236133), (+1.09517050, +0.684723020), (+1.27919960, +0.987547636), (+1.56138539, +0.417937219), (+1.82110083, +0.271674961), (+1.87753558, +0.923349977), (+1.25692809, +0.399388850), (+1.92362165, +0.877990127), (+1.47921777, +0.768719018), (+1.40711045, +0.439919561), (+1.48806453, +0.566953182), (+1.92320085, +0.269256055), (+1.68985057, +0.348689705), (+1.86898065, +0.103491992), (+1.15623641, +0.192840964), (+1.97426653, +0.243214503), (+1.34635305, +0.512811661), (+1.96872318, +0.687351227), (+1.12904978, +0.190056756), (+1.54338253, +0.843733311), (+1.87741482, +0.781754017), (+1.58612108, +0.924536467), (+1.59401798, +0.305514365), (+1.61335814, +0.951383710), (+1.36662984, +0.653753340), (+1.51939440, +0.304568589), (+1.60781717, +0.392411411), (+1.72869897, +0.494312525), (+1.56681275, +0.199020803), (+1.98877358, +0.764280319), (+1.38840628, +0.168674514), (+1.01917076, +0.712672532), (+1.30150783, +0.631850600), (+1.89562941, +0.874550283), (+1.74518633, +0.769829035), (+1.30930400, +0.132590786), (+1.32012677, +0.814105868), (+1.50213289, +0.244354188), (+1.06989300, +0.272728980), (+1.24146175, +0.611428797), (+1.51787066, +0.308743060), (+1.62279630, +0.330386221), (+1.54465747, +0.356355786), (+1.24692249, +0.904499233), (+1.84842753, +0.522753000), (+1.32894540, +0.639030993), (+1.90354359, +0.578615665), (+1.10572577, +0.150998816), (+1.19408298, +0.279882699), (+1.81823564, +0.633820772), (+1.66833854, +0.226875812), (+1.99200702, +0.335895181), (+1.70004177, +0.236870050E-1), (+1.69536185, +0.854159713), (+1.71382987, +0.825032413), (+1.37814236, +0.423573434), (+1.69239438, +0.487396866), (+1.33342791, +0.261447042), (+1.74726868, +0.917256325E-1), (+1.42477632, +0.302263349), (+1.66209590, +0.705818295), (+1.27793396, +0.647675276), (+1.32098651, +0.776716530), (+1.30240250, +0.891864300E-2), (+1.06791580, +0.747151494), (+1.64405799, +0.208811760), (+1.04311848, +0.608524442), (+1.79520583, +0.204218805), (+1.73364437, +0.956647515), (+1.51841640, +0.342005342), (+1.31871450, +0.185925081), (+1.73752832, +0.107100308E-1), (+1.69234920, +0.110917270), (+1.23210645, +0.496393472), (-0.596046448E-7, +0.298023224E-7), (+0.596046448E-7, -0.894069672E-7), (+0.417232513E-6, +0.894069672E-7), (+0.298023224E-6, +0.558793545E-7), (-0.596046448E-7, +0.208616257E-6), (+0.119209290E-6, +0.894069672E-7), (+0.178813934E-6, +0.894069672E-7), (+0.119209290E-6, +0.387430191E-6), (-0.596046448E-7, +0.342726707E-6), (-0.119209290E-6, +0.119209290E-6), (+0.00000000, +0.268220901E-6), (+0.596046448E-7, +0.387430191E-6), (+0.178813934E-6, +0.298023224E-7), (+0.357627869E-6, +0.00000000), (+0.596046448E-7, +0.596046448E-7), (+0.596046448E-7, +0.596046448E-7), (+0.178813934E-6, +0.447034836E-7), (+0.238418579E-6, +0.745058060E-7), (+0.596046448E-7, +0.178813934E-6), (+0.00000000, +0.208616257E-6), (+0.298023224E-6, +0.163912773E-6), (+0.417232513E-6, +0.238418579E-6), (+0.119209290E-6, +0.149011612E-6), (+0.298023224E-6, +0.298023224E-6), (+0.596046448E-7, +0.357627869E-6), (+0.178813934E-6, +0.134110451E-6), (+0.596046448E-7, +0.149011612E-6), (+0.178813934E-6, +0.298023224E-6), (+0.357627869E-6, -0.745058060E-7), (+0.417232513E-6, -0.178813934E-6), (+0.178813934E-6, +0.149011612E-7), (+0.298023224E-6, -0.447034836E-7), (+0.596046448E-7, -0.745058060E-7), (+0.238418579E-6, -0.596046448E-7), (+0.178813934E-6, +0.894069672E-7), (+0.298023224E-6, -0.596046448E-7)

317reltol = sqrt(epsilon(1._TKC))

318reltol

319+0.345266977E-3

320isClose(data, atad(1:size(data)), reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+74

327data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

328data

329(+1.3029156922182894, +0.97340589142527900), (+1.2337008302400494, +0.53363159650343250), (+1.4164546239718714, +0.18973128523428773), (+1.2966444652182294, +0.79497114511979738), (+1.4044402448429023, +0.65555593810522728), (+1.0428534044819902, +0.26879108727302603), (+1.9212245416333997, +0.79721010915699608E-1), (+1.6912341985105699, +0.56606429562584659), (+1.3732846971797759, +0.68538821444014042), (+1.4067075432736154, +0.60384187103392228), (+1.3304886343538112, +0.68667000644050602), (+1.8184062827056098, +0.22291388373472587), (+1.0781299196738714, +0.16173574335418195), (+1.6340696333115090, +0.95554258690288674), (+1.7968502921467766, +0.42460863914474867), (+1.0167664192018262, +0.26134374301149954E-1), (+1.9086701506012980, +0.37826488927348745E-1), (+1.9892424491097072, +0.24455270989513178), (+1.8424161492043032, +0.82965420177178895), (+1.4353043851850935, +0.90327229553808375), (+1.0824081534721375, +0.33067555941843252), (+1.8282917219772283, +0.82912009506666107E-1), (+1.2612773405482569, +0.63552090113976722), (+1.9875148627219625, +0.71255573189575649E-1), (+1.1432519869512294, +0.36535635637584307), (+1.9843211809612178, +0.65522687423584680), (+1.9934657602513437, +0.80957664052982348), (+1.1401982130011179, +0.14774213307386397), (+1.1538207811664472, +0.33036943901924398), (+1.0679685279125501, +0.16661366913598430E-1), (+1.9587554533086280, +0.44325021930647057), (+1.2393460278873434, +0.49740603886299373), (+1.7142389349088667, +0.48189973231254113), (+1.9968258138718649, +0.27835000360219042), (+1.4164466816474266, +0.60093961322036593), (+1.8566913207225761, +0.43199579694648393), (+1.9293367077153760, +0.29465447316998528), (+1.7192421798648423, +0.75967203180583442), (+1.7382877513891981, +0.13259491787894184), (+1.2525083932497381, +0.20285207713541209), (+1.6321354608219454, +0.55081884557154470), (+1.2439846849117950, +0.32123463163215848), (+1.8148361654874416, +0.43272370315977771), (+1.8409037990023771, +0.92137268893126878), (+1.9539988348823742, +0.57553864226827267), (+1.9720756956129302, +0.60439669617019709), (+1.4830653816446384, +0.20661082082714899), (+1.0176506118959603, +0.41103602507013581), (+1.3461432755627305, +0.87007942049909814), (+1.1380381856973871, +0.56736746722184161), (+1.7849169590986051, +0.23357838644383988), (+1.9974825615168710, +0.14131614655691460E-1), (+1.6785682064564051, +0.10991625847413400), (+1.4942898237856921, +0.21011295812101671), (+1.4061898965406052, +0.87257361230976738), (+1.5031549569507685, +0.75105708910308566), (+1.4051949736883538, +0.54948202900161192), (+1.6343711174880220, +0.63923020430529320), (+1.7617598810742621, +0.53614264803780165), (+1.8605550040655729, +0.81670481709969500), (+1.1446942662334232, +0.45650973705226627), (+1.7246468860616448, +0.39976062542622781), (+1.2859443592748445, +0.12790619360423605), (+1.2774367224269967, +0.39827347928657675), (+1.3249154095498474, +0.80160454664621916), (+1.9942945091751019, +0.43363311279205952), (+1.8287810413177810, +0.14086617736600759), (+1.9358981015324259, +0.40226920915548681), (+1.1190976576877083, +0.65018347915892893E-1), (+1.4013913628502206, +0.82872869208599209), (+1.7752567380366493, +0.58738480472728882), (+1.3322032669176118, +0.29152422206065065E-1), (+1.0828975260947387, +0.36862761830995938), (+1.9157540225313925, +0.43197994736695411)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.3029156922182894, +0.97340589142527900), (+1.2337008302400494, +0.53363159650343284), (+1.4164546239718714, +0.18973128523428795), (+1.2966444652182296, +0.79497114511979761), (+1.4044402448429021, +0.65555593810522739), (+1.0428534044819902, +0.26879108727302631), (+1.9212245416333993, +0.79721010915699830E-1), (+1.6912341985105703, +0.56606429562584681), (+1.3732846971797761, +0.68538821444014042), (+1.4067075432736151, +0.60384187103392228), (+1.3304886343538112, +0.68667000644050624), (+1.8184062827056100, +0.22291388373472629), (+1.0781299196738714, +0.16173574335418203), (+1.6340696333115088, +0.95554258690288696), (+1.7968502921467762, +0.42460863914474911), (+1.0167664192018264, +0.26134374301150204E-1), (+1.9086701506012980, +0.37826488927349022E-1), (+1.9892424491097067, +0.24455270989513223), (+1.8424161492043027, +0.82965420177178884), (+1.4353043851850937, +0.90327229553808386), (+1.0824081534721373, +0.33067555941843263), (+1.8282917219772281, +0.82912009506666398E-1), (+1.2612773405482562, +0.63552090113976711), (+1.9875148627219623, +0.71255573189575566E-1), (+1.1432519869512296, +0.36535635637584313), (+1.9843211809612173, +0.65522687423584680), (+1.9934657602513437, +0.80957664052982359), (+1.1401982130011179, +0.14774213307386413), (+1.1538207811664472, +0.33036943901924409), (+1.0679685279125501, +0.16661366913598694E-1), (+1.9587554533086275, +0.44325021930647057), (+1.2393460278873434, +0.49740603886299373), (+1.7142389349088669, +0.48189973231254091), (+1.9968258138718646, +0.27835000360219042), (+1.4164466816474266, +0.60093961322036571), (+1.8566913207225761, +0.43199579694648405), (+1.9293367077153760, +0.29465447316998500), (+1.7192421798648421, +0.75967203180583420), (+1.7382877513891981, +0.13259491787894148), (+1.2525083932497383, +0.20285207713541198), (+1.6321354608219454, +0.55081884557154459), (+1.2439846849117950, +0.32123463163215865), (+1.8148361654874416, +0.43272370315977748), (+1.8409037990023767, +0.92137268893126900), (+1.9539988348823742, +0.57553864226827223), (+1.9720756956129299, +0.60439669617019698), (+1.4830653816446382, +0.20661082082714838), (+1.0176506118959603, +0.41103602507013559), (+1.3461432755627305, +0.87007942049909770), (+1.1380381856973871, +0.56736746722184117), (+1.7849169590986049, +0.23357838644383969), (+1.9974825615168712, +0.14131614655691321E-1), (+1.6785682064564049, +0.10991625847413344), (+1.4942898237856919, +0.21011295812101632), (+1.4061898965406052, +0.87257361230976671), (+1.5031549569507687, +0.75105708910308522), (+1.4051949736883538, +0.54948202900161158), (+1.6343711174880218, +0.63923020430529309), (+1.7617598810742621, +0.53614264803780110), (+1.8605550040655727, +0.81670481709969445), (+1.1446942662334232, +0.45650973705226572), (+1.7246468860616442, +0.39976062542622715), (+1.2859443592748443, +0.12790619360423558), (+1.2774367224269967, +0.39827347928657642), (+1.3249154095498477, +0.80160454664621916), (+1.9942945091751016, +0.43363311279205946), (+1.8287810413177810, +0.14086617736600771), (+1.9358981015324261, +0.40226920915548647), (+1.1190976576877083, +0.65018347915892671E-1), (+1.4013913628502204, +0.82872869208599176), (+1.7752567380366495, +0.58738480472728838), (+1.3322032669176123, +0.29152422206064621E-1), (+1.0828975260947384, +0.36862761830995927), (+1.9157540225313918, +0.43197994736695422), (+0.0000000000000000, -0.44408920985006262E-15), (-0.11102230246251565E-15, -0.69388939039072284E-15), (+0.33306690738754696E-15, -0.27755575615628914E-16), (+0.44408920985006262E-15, -0.55511151231257827E-15), (+0.55511151231257827E-15, -0.33306690738754696E-15), (+0.22204460492503131E-15, -0.36082248300317588E-15), (+0.33306690738754696E-15, -0.55511151231257827E-16), (+0.33306690738754696E-15, -0.44408920985006262E-15), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, -0.38857805861880479E-15), (+0.0000000000000000, -0.83266726846886741E-16), (+0.22204460492503131E-15, -0.37470027081099033E-15), (+0.66613381477509392E-15, +0.55511151231257827E-16), (+0.33306690738754696E-15, +0.27755575615628914E-16), (+0.0000000000000000, -0.11102230246251565E-15), (-0.22204460492503131E-15, -0.33306690738754696E-15), (+0.0000000000000000, -0.11102230246251565E-15), (+0.22204460492503131E-15, -0.22204460492503131E-15), (+0.22204460492503131E-15, -0.27755575615628914E-16), (+0.22204460492503131E-15, -0.13877787807814457E-16), (+0.33306690738754696E-15, +0.22204460492503131E-15), (+0.44408920985006262E-15, -0.83266726846886741E-16), (+0.22204460492503131E-15, +0.24980018054066022E-15), (+0.0000000000000000, +0.83266726846886741E-16), (-0.11102230246251565E-15, +0.33306690738754696E-15), (+0.33306690738754696E-15, +0.13877787807814457E-15), (+0.0000000000000000, +0.27755575615628914E-15), (-0.22204460492503131E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, +0.36082248300317588E-15), (+0.33306690738754696E-15, +0.16653345369377348E-15), (-0.33306690738754696E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, -0.55511151231257827E-16), (+0.0000000000000000, +0.13877787807814457E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.13877787807814457E-15), (+0.11102230246251565E-15, +0.33306690738754696E-15), (+0.44408920985006262E-15, +0.16653345369377348E-15), (+0.11102230246251565E-15, +0.47184478546569153E-15), (+0.66613381477509392E-15, +0.19428902930940239E-15), (+0.22204460492503131E-15, +0.44408920985006262E-15), (+0.33306690738754696E-15, +0.48572257327350599E-15), (+0.33306690738754696E-15, +0.77715611723760958E-15), (+0.11102230246251565E-15, +0.49960036108132044E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.0000000000000000, +0.0000000000000000), (+0.0000000000000000, +0.61062266354383610E-15), (+0.44408920985006262E-15, +0.49960036108132044E-15), (+0.11102230246251565E-15, +0.52735593669694936E-15), (+0.44408920985006262E-15, +0.99920072216264089E-15), (+0.33306690738754696E-15, +0.83266726846886741E-15), (+0.44408920985006262E-15, +0.58286708792820718E-15)

334reltol = sqrt(epsilon(1._TKC))

335reltol

336+0.14901161193847656E-7

337isClose(data, atad(1:size(data)), reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+5

344data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

345data

346(+1.23328469395398444967953608758262914, +0.182450365211739217753142909904452738), (+1.94651518336821577608967640071505610, +0.634592982789124688318282030169334303), (+1.96818489623391835589578422206707671, +0.416460397889248358457196452959984633), (+1.00221645582117024660224660883399592, +0.870645598391896191183926587873749934), (+1.39148011292498951781470401979217470, +0.238902083624760765533878253412770732)

347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.23328469395398444967953608758262914, +0.182450365211739217753142909904452714), (+1.94651518336821577608967640071505590, +0.634592982789124688318282030169334399), (+1.96818489623391835589578422206707671, +0.416460397889248358457196452959984633), (+1.00221645582117024660224660883399592, +0.870645598391896191183926587873749742), (+1.39148011292498951781470401979217470, +0.238902083624760765533878253412770708), (+0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-34), (+0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33)

351reltol = sqrt(epsilon(1._TKC))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, atad(1:size(data)), reltol = reltol)

355T, T, T, T, T

356call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+26

361data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

362data

363+1.98692155, +1.05780268, +1.50604510, +1.63654065, +1.29159379, +1.58240533, +1.75077868, +1.72499037, +1.46580589, +1.00805736, +1.15122235, +1.33990550, +1.06753480, +1.96022964, +1.14683867, +1.89165187, +1.43463492, +1.85402775, +1.91431510, +1.03258884, +1.16728997, +1.90950656, +1.03492892, +1.40366066, +1.71308160, +1.88729763

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.98692155, +1.05780256, +1.50604498, +1.63654089, +1.29159343, +1.58240533, +1.75077820, +1.72499061, +1.46580565, +1.00805736, +1.15122235, +1.33990550, +1.06753492, +1.96022940, +1.14683867, +1.89165163, +1.43463469, +1.85402763, +1.91431487, +1.03258896, +1.16728985, +1.90950656, +1.03492856, +1.40366077, +1.71308148, +1.88729763, -0.357627869E-6, +0.178813934E-6, -0.596046448E-7, +0.476837158E-6, +0.178813934E-6, +0.238418579E-6

368reltol = sqrt(epsilon(1._TKC))

369reltol

370+0.345266977E-3

371isClose(data, atad(1:size(data)), reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+38

378data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

379data

380+1.9745088409275771, +1.3553105056361512, +1.1910798605688666, +1.7835582349699757, +1.8098232165615722, +1.2559615955596293, +1.4143964184640714, +1.7673448943696368, +1.8384292025748383, +1.6925811939955535, +1.6888471331178709, +1.7544592190641237, +1.8691387605200225, +1.5847775707764984, +1.4604937635221300, +1.5450143877276266, +1.8879566948547251, +1.5699550298845986, +1.5079785937610790, +1.0925988585130226, +1.0653744218848269, +1.3014049193021808, +1.8771810015818029, +1.0309026662280527, +1.7658317178430256, +1.8753520570459972, +1.0049660592738827, +1.6956407737977246, +1.2487784554594299, +1.3330068777931978, +1.3000325754091469, +1.7369015722305774, +1.8122946272989184, +1.7848163688248158, +1.6559311860697226, +1.4848667536934921, +1.2149477899248302, +1.1437503925888715

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.9745088409275771, +1.3553105056361519, +1.1910798605688664, +1.7835582349699761, +1.8098232165615722, +1.2559615955596295, +1.4143964184640712, +1.7673448943696370, +1.8384292025748383, +1.6925811939955542, +1.6888471331178705, +1.7544592190641239, +1.8691387605200223, +1.5847775707764984, +1.4604937635221300, +1.5450143877276266, +1.8879566948547253, +1.5699550298845988, +1.5079785937610792, +1.0925988585130222, +1.0653744218848269, +1.3014049193021806, +1.8771810015818027, +1.0309026662280527, +1.7658317178430254, +1.8753520570459967, +1.0049660592738827, +1.6956407737977242, +1.2487784554594299, +1.3330068777931974, +1.3000325754091471, +1.7369015722305767, +1.8122946272989187, +1.7848163688248162, +1.6559311860697228, +1.4848667536934919, +1.2149477899248302, +1.1437503925888712, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.44408920985006262E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.55511151231257827E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.0000000000000000, +0.12212453270876722E-14, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.77715611723760958E-15

385reltol = sqrt(epsilon(1._TKC))

386reltol

387+0.14901161193847656E-7

388isClose(data, atad(1:size(data)), reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+60

395data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

396data

397+1.63154414093705413927481371184555634, +1.99370247364844193148938914906884584, +1.78305011596369394759183600493283139, +1.89829697868922206036945527615527377, +1.04821430319054133389260595300284420, +1.15895330208823523772461984427098402, +1.84816203177623720050213596170808306, +1.79218732189980092289917310543312996, +1.25955470723495008561112054376776424, +1.41564658749906131256998964385769994, +1.48689944356008291888567662134548045, +1.63416558826594898939380470034067369, +1.96705644826875357938973195572747981, +1.78253511210993296553593285582981060, +1.93532498615972914841631608007986864, +1.48846632396110177725435420548631942, +1.81915332544572127810710897637309681, +1.06488343654449485382842845882363268, +1.74626606931873861127004815069038480, +1.41893460869406521840942944027673620, +1.72052261754001735972327466200085664, +1.67317762104662553844595693457831920, +1.82030981353180593826335212380553733, +1.68940156444353208901504227450832047, +1.89437042961495111453810944053141902, +1.01124985190226377742553224089052691, +1.57450598259023705576010588426645572, +1.76912602593114756962683908786202621, +1.13659879808629000477504559328405136, +1.16738218049650087817521207791045931, +1.54343174366290150686104686198309083, +1.53540852649633618488382525732967278, +1.55523396710202051644602257831719785, +1.16443794915440678522250789906075649, +1.58241745768274438898736510519074017, +1.76119415366695600298886751680851859, +1.70008292085813982737256900700706456, +1.82552264205687059949193247400889509, +1.58723162936379338352218168440638972, +1.57710272443001607524370439731614608, +1.30634284342541440418270471890744595, +1.89158127164757291958857102383731950, +1.14046245947407344239865629083655439, +1.26001224705387878244054406014566865, +1.77215001032092816609985227566968868, +1.56055301201344367665097567719112227, +1.82644063216787713988655831199160867, +1.24374110290536235355940111415260779, +1.09496657766921542056557683366078377, +1.97750935460634157229762112683734337, +1.82501244029066891754128128934653729, +1.11635873205716571376633250034811479, +1.85258449089012543502912633008136807, +1.52872017913522166486084259460236584, +1.83581078880213391784003860661717337, +1.84814373964447761896736018320283273, +1.18675241540254925021768998789763177, +1.03041566521340741400214331579220151, +1.54893074172888318193874625513351163, +1.94764448413702040832615295874647800

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.63154414093705413927481371184555634, +1.99370247364844193148938914906884565, +1.78305011596369394759183600493283139, +1.89829697868922206036945527615527396, +1.04821430319054133389260595300284439, +1.15895330208823523772461984427098383, +1.84816203177623720050213596170808325, +1.79218732189980092289917310543313015, +1.25955470723495008561112054376776443, +1.41564658749906131256998964385769994, +1.48689944356008291888567662134548026, +1.63416558826594898939380470034067369, +1.96705644826875357938973195572748058, +1.78253511210993296553593285582981002, +1.93532498615972914841631608007986902, +1.48846632396110177725435420548631903, +1.81915332544572127810710897637309700, +1.06488343654449485382842845882363229, +1.74626606931873861127004815069038480, +1.41893460869406521840942944027673639, +1.72052261754001735972327466200085664, +1.67317762104662553844595693457831901, +1.82030981353180593826335212380553733, +1.68940156444353208901504227450832047, +1.89437042961495111453810944053141902, +1.01124985190226377742553224089052652, +1.57450598259023705576010588426645572, +1.76912602593114756962683908786202621, +1.13659879808629000477504559328405097, +1.16738218049650087817521207791045893, +1.54343174366290150686104686198309064, +1.53540852649633618488382525732967278, +1.55523396710202051644602257831719785, +1.16443794915440678522250789906075629, +1.58241745768274438898736510519074037, +1.76119415366695600298886751680851878, +1.70008292085813982737256900700706456, +1.82552264205687059949193247400889490, +1.58723162936379338352218168440638992, +1.57710272443001607524370439731614646, +1.30634284342541440418270471890744633, +1.89158127164757291958857102383731950, +1.14046245947407344239865629083655420, +1.26001224705387878244054406014566865, +1.77215001032092816609985227566968906, +1.56055301201344367665097567719112208, +1.82644063216787713988655831199160867, +1.24374110290536235355940111415260798, +1.09496657766921542056557683366078396, +1.97750935460634157229762112683734279, +1.82501244029066891754128128934653710, +1.11635873205716571376633250034811498, +1.85258449089012543502912633008136807, +1.52872017913522166486084259460236565, +1.83581078880213391784003860661717318, +1.84814373964447761896736018320283292, +1.18675241540254925021768998789763177, +1.03041566521340741400214331579220113, +1.54893074172888318193874625513351163, +1.94764448413702040832615295874647800, -0.962964972193617926527988971292463659E-34, -0.674075480535532548569592279904724561E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33

402reltol = sqrt(epsilon(1._TKC))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, atad(1:size(data)), reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+12

412data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

413data

414(+1.59387636, +0.667777121), (+1.92029738, +0.455795527), (+1.09146547, +0.843129754), (+1.84373569, +0.567078888), (+1.98658514, +0.622641325), (+1.85589361, +0.950640976), (+1.50436831, +0.216255248), (+1.57031560, +0.694829404), (+1.03489494, +0.735510349), (+1.70953798, +0.189169049E-1), (+1.91169596, +0.417989492E-1), (+1.14663100, +0.648380935)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.59387636, +0.667777002), (+1.92029762, +0.455795676), (+1.09146559, +0.843129754), (+1.84373558, +0.567079008), (+1.98658514, +0.622641146), (+1.85589373, +0.950640917), (+1.50436854, +0.216255128), (+1.57031560, +0.694829226), (+1.03489494, +0.735510290), (+1.70953798, +0.189169049E-1), (+1.91169584, +0.417988598E-1), (+1.14663088, +0.648380816), (-0.596046448E-7, +0.596046448E-7), (-0.119209290E-6, -0.298023224E-7), (+0.238418579E-6, +0.596046448E-7), (+0.178813934E-6, +0.149011612E-6)

419reltol = sqrt(epsilon(1._TKC))

420reltol

421+0.345266977E-3

422isClose(data, atad(1:size(data)), reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+89

429data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

430data

431(+1.4140367800467932, +0.72246270386635647), (+1.0934230876765803, +0.38829311243285702E-1), (+1.4369957181406341, +0.83874840125512717), (+1.5369147415344999, +0.88497350806191299), (+1.2405643654177503, +0.50418551296902026), (+1.6747484673578330, +0.74828896199249018), (+1.6491039307087305, +0.48027322003785178), (+1.7547771007894732, +0.90773044019554994), (+1.0153629504816448, +0.38168536410046694), (+1.2513121819651811, +0.74214397412205679), (+1.7131480254149352, +0.64395999635107104), (+1.8409185952333367, +0.18689137683922818), (+1.5465915831191897, +0.39705420293207516), (+1.5919124130083031, +0.56812982960312353), (+1.9210104033716127, +0.94992194297016352), (+1.3482018037567833, +0.92087821636734035), (+1.6601549993815570, +0.60129746241001847), (+1.9208205063676216, +0.99063512415949384), (+1.1595616632470827, +0.42602961828539387), (+1.0851165406552363, +0.18641954359508617), (+1.9109959129986247, +0.87092868082935460), (+1.5711863875131578, +0.27453527426223412), (+1.0483528180128303, +0.48849351604461888), (+1.3136469111493874, +0.30934081599129615), (+1.4401294224635157, +0.60761942982221906), (+1.3653781804815424, +0.22582012833682408), (+1.6683449709088527, +0.64045831459440961), (+1.1978312778555695, +0.69139830455083873E-2), (+1.2897819518208897, +0.62366066924748165), (+1.7174476241149177, +0.37491654345296455), (+1.0026227940825652, +0.49184266021353318), (+1.9945295583085239, +0.47235855918889380), (+1.7412475993796508, +0.47360114583127333), (+1.4555573089891745, +0.60783221576081570), (+1.9906569333925710, +0.44076666298468437), (+1.4556177311568645, +0.15318015921689565), (+1.8647183575405313, +0.69534197865262803), (+1.9352861769724816, +0.80921619103247067), (+1.8934863012993355, +0.96176683726277112), (+1.7863400812591230, +0.75705936539811081), (+1.4394606595010750, +0.81719087428893800), (+1.7400583201179827, +0.40061346070628023), (+1.0467056989725434, +0.46911122007113337E-1), (+1.2968727479933801, +0.91409558452621631), (+1.2227522650828779, +0.32508847602580349), (+1.4374699705151399, +0.88633072508066624), (+1.7669719222269880, +0.68633701202421926), (+1.6803906711557297, +0.24108801432433213), (+1.5690149183095534, +0.26125149470727949), (+1.4665557068482280, +0.84451818652919375), (+1.5134620671847485, +0.27071535672613423), (+1.3443756791880959, +0.64887852531013035E-1), (+1.6925745330968698, +0.47043162760119150), (+1.0325773195159922, +0.88980759968259193), (+1.7990776817417424, +0.83637971632348806), (+1.8442596622138394, +0.18916204691417215), (+1.9943729201371667, +0.56275670667923472), (+1.9839479005760605, +0.26685603365769761), (+1.9633829871361455, +0.13449225427677802), (+1.3806973747107025, +0.54264959886827491), (+1.1969449112442079, +0.29617821151006396), (+1.5225440015220750, +0.96023301398290972), (+1.0215450956293317, +0.99225850627622170), (+1.8082405308434950, +0.93115447490396486), (+1.7183261528903595, +0.99497158848809641), (+1.6590405211237895, +0.93993709341921872), (+1.6626602069669660, +0.72017467832689708), (+1.0344245073428080, +0.80475166625601469), (+1.2426200780027135, +0.64883009604300190), (+1.2068832407435570, +0.73325138822527336), (+1.1803854425216314, +0.71779469525880968), (+1.3821349821811131, +0.64684249097777813), (+1.3650568012556219, +0.54289216290526021), (+1.0315808791030134, +0.80798311538095158), (+1.3242676422563711, +0.67437274808230596), (+1.6886602370259971, +0.38039440081804465), (+1.2033394487477636, +0.19136378788540032), (+1.9828852936724055, +0.31160275030975515), (+1.8831981845118813, +0.40487012017570634), (+1.1223066535722122, +0.93300558234801878E-1), (+1.7330614800507678, +0.25684706404780600E-1), (+1.8481911699900762, +0.83010895301841825), (+1.5707720898957493, +0.35658876521715532), (+1.6349662962141451, +0.91001412175950258E-1), (+1.9140818345848447, +0.25122842778227716), (+1.2324739184771820, +0.81464187665241983), (+1.4467997289305921, +0.75942339471929965), (+1.5585288701224109, +0.94316586229404198E-1), (+1.3484977238389635, +0.74939758787533661)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.4140367800467932, +0.72246270386635647), (+1.0934230876765805, +0.38829311243285980E-1), (+1.4369957181406339, +0.83874840125512717), (+1.5369147415345006, +0.88497350806191322), (+1.2405643654177503, +0.50418551296902026), (+1.6747484673578334, +0.74828896199249040), (+1.6491039307087301, +0.48027322003785167), (+1.7547771007894737, +0.90773044019555016), (+1.0153629504816453, +0.38168536410046683), (+1.2513121819651813, +0.74214397412205690), (+1.7131480254149349, +0.64395999635107137), (+1.8409185952333371, +0.18689137683922841), (+1.5465915831191894, +0.39705420293207538), (+1.5919124130083033, +0.56812982960312408), (+1.9210104033716122, +0.94992194297016341), (+1.3482018037567836, +0.92087821636734035), (+1.6601549993815568, +0.60129746241001847), (+1.9208205063676211, +0.99063512415949395), (+1.1595616632470824, +0.42602961828539376), (+1.0851165406552368, +0.18641954359508620), (+1.9109959129986247, +0.87092868082935460), (+1.5711863875131575, +0.27453527426223423), (+1.0483528180128299, +0.48849351604461888), (+1.3136469111493874, +0.30934081599129609), (+1.4401294224635157, +0.60761942982221928), (+1.3653781804815424, +0.22582012833682413), (+1.6683449709088523, +0.64045831459440961), (+1.1978312778555700, +0.69139830455086093E-2), (+1.2897819518208897, +0.62366066924748154), (+1.7174476241149175, +0.37491654345296499), (+1.0026227940825652, +0.49184266021353296), (+1.9945295583085236, +0.47235855918889386), (+1.7412475993796508, +0.47360114583127311), (+1.4555573089891745, +0.60783221576081559), (+1.9906569333925710, +0.44076666298468420), (+1.4556177311568650, +0.15318015921689554), (+1.8647183575405317, +0.69534197865262792), (+1.9352861769724818, +0.80921619103247022), (+1.8934863012993355, +0.96176683726277079), (+1.7863400812591235, +0.75705936539811047), (+1.4394606595010750, +0.81719087428893789), (+1.7400583201179824, +0.40061346070627984), (+1.0467056989725430, +0.46911122007113143E-1), (+1.2968727479933804, +0.91409558452621631), (+1.2227522650828779, +0.32508847602580349), (+1.4374699705151397, +0.88633072508066579), (+1.7669719222269875, +0.68633701202421893), (+1.6803906711557297, +0.24108801432433213), (+1.5690149183095534, +0.26125149470727937), (+1.4665557068482276, +0.84451818652919353), (+1.5134620671847481, +0.27071535672613389), (+1.3443756791880959, +0.64887852531013049E-1), (+1.6925745330968700, +0.47043162760119117), (+1.0325773195159924, +0.88980759968259160), (+1.7990776817417427, +0.83637971632348740), (+1.8442596622138394, +0.18916204691417177), (+1.9943729201371667, +0.56275670667923439), (+1.9839479005760603, +0.26685603365769750), (+1.9633829871361448, +0.13449225427677761), (+1.3806973747107028, +0.54264959886827491), (+1.1969449112442079, +0.29617821151006374), (+1.5225440015220753, +0.96023301398290917), (+1.0215450956293317, +0.99225850627622092), (+1.8082405308434948, +0.93115447490396397), (+1.7183261528903597, +0.99497158848809653), (+1.6590405211237893, +0.93993709341921883), (+1.6626602069669658, +0.72017467832689697), (+1.0344245073428084, +0.80475166625601480), (+1.2426200780027137, +0.64883009604300179), (+1.2068832407435575, +0.73325138822527336), (+1.1803854425216314, +0.71779469525880946), (+1.3821349821811137, +0.64684249097777813), (+1.3650568012556221, +0.54289216290525999), (+1.0315808791030132, +0.80798311538095147), (+1.3242676422563706, +0.67437274808230585), (+1.6886602370259971, +0.38039440081804488), (+1.2033394487477633, +0.19136378788540034), (+1.9828852936724055, +0.31160275030975515), (+1.8831981845118813, +0.40487012017570578), (+1.1223066535722126, +0.93300558234801823E-1), (+1.7330614800507675, +0.25684706404780433E-1), (+1.8481911699900757, +0.83010895301841803), (+1.5707720898957491, +0.35658876521715510), (+1.6349662962141451, +0.91001412175950119E-1), (+1.9140818345848449, +0.25122842778227716), (+1.2324739184771825, +0.81464187665241927), (+1.4467997289305923, +0.75942339471929876), (+1.5585288701224114, +0.94316586229403920E-1), (+1.3484977238389637, +0.74939758787533650), (-0.11102230246251565E-15, -0.40245584642661925E-15), (+0.11102230246251565E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, -0.49960036108132044E-15), (+0.55511151231257827E-15, -0.16653345369377348E-15), (+0.77715611723760958E-15, -0.58286708792820718E-15), (+0.44408920985006262E-15, -0.16653345369377348E-15), (+0.88817841970012523E-15, -0.27755575615628914E-15), (-0.11102230246251565E-15, +0.13877787807814457E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (-0.22204460492503131E-15, +0.27755575615628914E-15), (+0.33306690738754696E-15, -0.20816681711721685E-15), (+0.11102230246251565E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.0000000000000000, +0.16653345369377348E-15), (+0.44408920985006262E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, -0.11102230246251565E-15), (-0.22204460492503131E-15, -0.55511151231257827E-16), (-0.22204460492503131E-15, +0.83266726846886741E-16), (+0.22204460492503131E-15, -0.11102230246251565E-15), (+0.22204460492503131E-15, +0.83266726846886741E-16), (+0.44408920985006262E-15, -0.55511151231257827E-16), (+0.0000000000000000, +0.33306690738754696E-15), (+0.88817841970012523E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.19428902930940239E-15), (+0.11102230246251565E-15, +0.27755575615628914E-15), (-0.11102230246251565E-15, +0.30531133177191805E-15), (+0.77715611723760958E-15, -0.97144514654701197E-16), (+0.66613381477509392E-15, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, +0.61062266354383610E-15), (+0.77715611723760958E-15, +0.37470027081099033E-15), (+0.0000000000000000, +0.11102230246251565E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.13877787807814457E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.33306690738754696E-15, +0.58286708792820718E-15), (+0.55511151231257827E-15, +0.66613381477509392E-15), (-0.11102230246251565E-15, +0.77715611723760958E-15), (+0.44408920985006262E-15, +0.72164496600635175E-15)

436reltol = sqrt(epsilon(1._TKC))

437reltol

438+0.14901161193847656E-7

439isClose(data, atad(1:size(data)), reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+45

446data = 1._TKC + getUnifRand((0._TKC, 0._TKC), (1._TKC, 1._TKC), lenData)

447data

448(+1.39662434836741366942225217769708791, +0.401238881678958643196295987389550886E-1), (+1.47793424684088465246585349871020773, +0.920632647965493746890799290732436128), (+1.56759656683379475429507898055413323, +0.566182020320652870114802862066674954), (+1.02100366696926994644721446247069261, +0.918130834212357340188321174644368632), (+1.97694900134394442340207206353288592, +0.657224512302163565987853982773008273), (+1.40539325864844360033060972677152230, +0.634718020508469263039493164195662644), (+1.93825535359896217020653255862215752, +0.581062887410756472227354664318475161), (+1.35301126848512020115144708097311732, +0.620870312221935443283115909854654525), (+1.63320957857109805638399574949191933, +0.613622602293366897635341761780052938), (+1.05768348188346839642658831102521723, +0.241952263015275667265791529178531713E-1), (+1.16803719360688009250864369749322065, +0.106832908015560987697003876336347073), (+1.50088685002089067927999238163995970, +0.677191121099979525080767709573951686), (+1.28241760998498057265965798414538716, +0.158268786549860452694747159354148737), (+1.52385135273909427567787612525764609, +0.339421220463124363211515015806689082), (+1.89387947993243527225585025238935636, +0.127655196209784122156079255646187631), (+1.92588425142815042608943745716689965, +0.443890855082179053803449703990979137), (+1.84004300741569835895111331184864616, +0.710245786738007866025110780159948031), (+1.64823688221671420178228278514459481, +0.217203166747376462251673754351258465), (+1.01765248869248824042024817791714899, +0.955931087567706901752943675777822589), (+1.49358655422484011238829506911419647, +0.291128349035096884130450633485516030E-1), (+1.78583009052030503230084725289341438, +0.610175799852120190762867537400805481), (+1.58824927948254469164020712343653336, +0.511835087008636746759882370322649161), (+1.78115809856697199926966325237911690, +0.279965174690825578702694444278120995), (+1.48712915886045180496796569858357694, +0.532517351584705387265720846020407783), (+1.23421626777246758115086185772781598, +0.587210080783707309444967999070830478), (+1.72115555070245913461668408461253734, +0.370396911594671816210687288888995829), (+1.14078373105591761413104578232990314, +0.667581008660560370526673891553299070), (+1.84420560720546274601422814146200338, +0.782282240200463582338828139701152370), (+1.10414620088336190685271895879612112, +0.181404849441998614112994014540660272), (+1.41764657286545910225124659209109860, +0.279379370652333630790498332203015270E-2), (+1.04884057701047948263589090411489576, +0.245397941277789121463735440785828175E-1), (+1.43112355644138351469168681867739546, +0.382666964983377268146641207631183030), (+1.85134612691738811321507622912482693, +0.359556357513893092753181002859610083), (+1.43927420065717596617624485155471691, +0.251998736800930967500289588928960855E-1), (+1.95116457158720796390332128515338327, +0.316739560223803436894632270079763010E-1), (+1.87928644405614084048506576702669740, +0.491893623349071856201486209876092454), (+1.35622998793950591151671954539237037, +0.933967719945316270876722612799041553E-1), (+1.69657045379747945747872292534318700, +0.461997562289431604286527526744111620), (+1.86802035348030070374662036920900924, +0.925093166528730980045072058199548154E-1), (+1.74325383532240367119750710902367526, +0.411277555133120565408126669337210236E-1), (+1.47665003133201230850614302319948884, +0.853310058594680155310401055885284236E-1), (+1.81660282076087709283230381479414786, +0.923169202185041349637523617080858461), (+1.36124802725698575306721674758628653, +0.113983828654717932378281954522743277), (+1.39870362171092200967782769522401573, +0.822994160234106741046484958939332198), (+1.36751984942500533192822760118555699, +0.453505170611102652003417480177930143)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.39662434836741366942225217769708791, +0.401238881678958643196295987389549683E-1), (+1.47793424684088465246585349871020754, +0.920632647965493746890799290732436128), (+1.56759656683379475429507898055413285, +0.566182020320652870114802862066674954), (+1.02100366696926994644721446247069242, +0.918130834212357340188321174644368632), (+1.97694900134394442340207206353288612, +0.657224512302163565987853982773008176), (+1.40539325864844360033060972677152249, +0.634718020508469263039493164195662644), (+1.93825535359896217020653255862215752, +0.581062887410756472227354664318474872), (+1.35301126848512020115144708097311732, +0.620870312221935443283115909854654140), (+1.63320957857109805638399574949191933, +0.613622602293366897635341761780052938), (+1.05768348188346839642658831102521723, +0.241952263015275667265791529178532676E-1), (+1.16803719360688009250864369749322065, +0.106832908015560987697003876336347025), (+1.50088685002089067927999238163995951, +0.677191121099979525080767709573951686), (+1.28241760998498057265965798414538735, +0.158268786549860452694747159354148785), (+1.52385135273909427567787612525764609, +0.339421220463124363211515015806689034), (+1.89387947993243527225585025238935617, +0.127655196209784122156079255646187727), (+1.92588425142815042608943745716689965, +0.443890855082179053803449703990979330), (+1.84004300741569835895111331184864616, +0.710245786738007866025110780159947838), (+1.64823688221671420178228278514459443, +0.217203166747376462251673754351258393), (+1.01765248869248824042024817791714918, +0.955931087567706901752943675777822492), (+1.49358655422484011238829506911419609, +0.291128349035096884130450633485514345E-1), (+1.78583009052030503230084725289341477, +0.610175799852120190762867537400805385), (+1.58824927948254469164020712343653355, +0.511835087008636746759882370322649257), (+1.78115809856697199926966325237911690, +0.279965174690825578702694444278121091), (+1.48712915886045180496796569858357694, +0.532517351584705387265720846020407879), (+1.23421626777246758115086185772781617, +0.587210080783707309444967999070830478), (+1.72115555070245913461668408461253715, +0.370396911594671816210687288888995637), (+1.14078373105591761413104578232990314, +0.667581008660560370526673891553298877), (+1.84420560720546274601422814146200338, +0.782282240200463582338828139701151888), (+1.10414620088336190685271895879612112, +0.181404849441998614112994014540660224), (+1.41764657286545910225124659209109860, +0.279379370652333630790498332203008048E-2), (+1.04884057701047948263589090411489556, +0.245397941277789121463735440785827934E-1), (+1.43112355644138351469168681867739527, +0.382666964983377268146641207631182838), (+1.85134612691738811321507622912482693, +0.359556357513893092753181002859610179), (+1.43927420065717596617624485155471671, +0.251998736800930967500289588928961818E-1), (+1.95116457158720796390332128515338327, +0.316739560223803436894632270079761565E-1), (+1.87928644405614084048506576702669740, +0.491893623349071856201486209876092454), (+1.35622998793950591151671954539237056, +0.933967719945316270876722612799040590E-1), (+1.69657045379747945747872292534318719, +0.461997562289431604286527526744112053), (+1.86802035348030070374662036920900962, +0.925093166528730980045072058199548394E-1), (+1.74325383532240367119750710902367526, +0.411277555133120565408126669337211680E-1), (+1.47665003133201230850614302319948884, +0.853310058594680155310401055885284718E-1), (+1.81660282076087709283230381479414786, +0.923169202185041349637523617080858461), (+1.36124802725698575306721674758628672, +0.113983828654717932378281954522743036), (+1.39870362171092200967782769522401592, +0.822994160234106741046484958939331716), (+1.36751984942500533192822760118555718, +0.453505170611102652003417480177930384), (-0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, +0.722223729145213444895991728469347744E-34), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, +0.168518870133883137142398069976181140E-33), (+0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, +0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, +0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (+0.288889491658085377958396691387739098E-33, -0.722223729145213444895991728469347744E-34), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (+0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34), (+0.288889491658085377958396691387739098E-33, -0.445371299639548291019194899222764442E-33), (+0.192592994438723585305597794258492732E-33, -0.264815367353244929795196967105427506E-33), (-0.192592994438723585305597794258492732E-33, -0.216667118743564033468797518540804323E-33), (-0.288889491658085377958396691387739098E-33, -0.120370621524202240815998621411557957E-33)

453reltol = sqrt(epsilon(1._TKC))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, atad(1:size(data)), reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+72

463data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

464data

465+1.15756345, +1.52442002, +1.18503690, +1.21702075, +1.93756914, +1.66473532, +1.74097943, +1.19628692, +1.42135561, +1.11899900, +1.68325019, +1.51779294, +1.62374520, +1.98795557, +1.23816919, +1.80583262, +1.88243079, +1.78038192, +1.55319440, +1.60828733, +1.51414609, +1.79750669, +1.05958581, +1.48250151, +1.34901595, +1.03470635, +1.07715917, +1.09712720, +1.13820982, +1.12201762, +1.23779535, +1.33003807, +1.52282798, +1.26532674, +1.16756022, +1.86658525, +1.61175108, +1.46592724, +1.97126627, +1.51839340, +1.74875140, +1.35528421, +1.27508962, +1.52464628, +1.03733897, +1.93766391, +1.13961625, +1.32439733, +1.96550798, +1.64400411, +1.43929505, +1.96541190, +1.39759910, +1.49467921, +1.75471067, +1.91439605, +1.40349793, +1.68893421, +1.01962674, +1.91360819, +1.71460652, +1.96392655, +1.83938658, +1.85075808, +1.80009842, +1.75349927, +1.10278070, +1.06040967, +1.04662776, +1.05772877, +1.98083186, +1.05872786

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.15756345, +1.52442014, +1.18503666, +1.21702087, +1.93756902, +1.66473484, +1.74097908, +1.19628680, +1.42135584, +1.11899900, +1.68324995, +1.51779294, +1.62374532, +1.98795533, +1.23816907, +1.80583239, +1.88243043, +1.78038192, +1.55319428, +1.60828733, +1.51414597, +1.79750657, +1.05958557, +1.48250139, +1.34901595, +1.03470647, +1.07715917, +1.09712744, +1.13820982, +1.12201762, +1.23779523, +1.33003831, +1.52282798, +1.26532662, +1.16756022, +1.86658514, +1.61175108, +1.46592700, +1.97126603, +1.51839304, +1.74875140, +1.35528421, +1.27508950, +1.52464616, +1.03733897, +1.93766379, +1.13961613, +1.32439709, +1.96550775, +1.64400411, +1.43929493, +1.96541178, +1.39759898, +1.49467897, +1.75471020, +1.91439581, +1.40349758, +1.68893397, +1.01962626, +1.91360819, +1.71460593, +1.96392655, +1.83938658, +1.85075819, +1.80009842, +1.75349939, +1.10278058, +1.06040990, +1.04662812, +1.05772877, +1.98083198, +1.05872786, -0.119209290E-6, +0.00000000, +0.596046448E-7, +0.178813934E-6, +0.00000000, +0.238418579E-6, +0.357627869E-6, +0.298023224E-6, +0.238418579E-6, -0.596046448E-7, +0.00000000, +0.178813934E-6, +0.119209290E-6, +0.596046448E-7, +0.238418579E-6, +0.357627869E-6, +0.298023224E-6, -0.119209290E-6, +0.596046448E-7, +0.00000000, +0.238418579E-6, -0.298023224E-6, +0.119209290E-6, -0.119209290E-6, -0.119209290E-6, +0.119209290E-6, -0.119209290E-6, +0.357627869E-6, -0.596046448E-7, +0.119209290E-6, +0.00000000, +0.536441803E-6, +0.00000000, +0.00000000, -0.596046448E-7, +0.357627869E-6, +0.119209290E-6, +0.00000000, +0.119209290E-6, +0.298023224E-6, +0.596046448E-7, +0.00000000, -0.119209290E-6, +0.238418579E-6, +0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.476837158E-6, +0.357627869E-6, +0.119209290E-6, +0.357627869E-6, +0.119209290E-6, +0.357627869E-6, +0.596046448E-7, -0.119209290E-6, +0.00000000

470reltol = sqrt(epsilon(1._TKC))

471reltol

472+0.345266977E-3

473isClose(data, atad(1:size(data)), reltol = reltol)

474T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+31

480data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

481data

482+1.3860002477973756, +1.2244337985239291, +1.1110658645284421, +1.3716288831144623, +1.0038762528818088, +1.2689031744174288, +1.9259687368236347, +1.0276991590224305, +1.5103944798761795, +1.2038133034052863, +1.5618954007556876, +1.1797600014514682, +1.9713271208864440, +1.5886588407986024, +1.5665046037652797, +1.2103745092683766, +1.4818027148880573, +1.2687139636900655, +1.5102487647536698, +1.6897705961120884, +1.5275182551708801, +1.9499677234965525, +1.3947485833341966, +1.5520269798954747, +1.9815039623086430, +1.9702792628167709, +1.9074447522991704, +1.0878430352891795, +1.7423112162953602, +1.8151878269079771, +1.1662607628773705

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.3860002477973752, +1.2244337985239293, +1.1110658645284417, +1.3716288831144621, +1.0038762528818086, +1.2689031744174291, +1.9259687368236345, +1.0276991590224305, +1.5103944798761790, +1.2038133034052863, +1.5618954007556876, +1.1797600014514682, +1.9713271208864436, +1.5886588407986024, +1.5665046037652797, +1.2103745092683764, +1.4818027148880568, +1.2687139636900657, +1.5102487647536691, +1.6897705961120881, +1.5275182551708799, +1.9499677234965522, +1.3947485833341966, +1.5520269798954742, +1.9815039623086430, +1.9702792628167709, +1.9074447522991700, +1.0878430352891795, +1.7423112162953602, +1.8151878269079771, +1.1662607628773705, +0.22204460492503131E-15

487reltol = sqrt(epsilon(1._TKC))

488reltol

489+0.14901161193847656E-7

490isClose(data, atad(1:size(data)), reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+11

497data = 1._TKC + getUnifRand(0._TKC, 1._TKC, lenData)

498data

499+1.33755511299786045091102817542280990, +1.98433325935605000460728013095942868, +1.26277355023587612820613902704878820, +1.17020543007261534134316103634587637, +1.06468988494801627602182571370558041, +1.77969550699722000570163397165910265, +1.91630967337052824444941142225757554, +1.95843817659167256898191573050903578, +1.69949184191617599223092827183353143, +1.37630387898624683506333892598099599, +1.22640819521585839806576486975415561

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.33755511299786045091102817542280990, +1.98433325935605000460728013095942868, +1.26277355023587612820613902704878820, +1.17020543007261534134316103634587656, +1.06468988494801627602182571370558041, +1.77969550699722000570163397165910265, +1.91630967337052824444941142225757535, +1.95843817659167256898191573050903578, +1.69949184191617599223092827183353143, +1.37630387898624683506333892598099599, +1.22640819521585839806576486975415561, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34

504reltol = sqrt(epsilon(1._TKC))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, atad(1:size(data)), reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

510

511

Test:: test_pm_fftnr

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, you must acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library, you must also ask the end users to cite this original ParaMonte library.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 250 of file pm_fftnr.F90.

The documentation for this interface was generated from the following file:

/home/amir/git/paramonte/src/fortran/main/pm_fftnr.F90